Scholarly article on topic 'Multi-granularity grooming using timing information in optical networks with waveband and TDM switching'

Multi-granularity grooming using timing information in optical networks with waveband and TDM switching Academic research paper on "Computer and information sciences"

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{"Dynamic traffic grooming" / "Optical Time Slot Interchanger (OTSI)" / "Holding time" / "Markov chain" / "Transient probability" / "Waveband switching (WBS)"}

Abstract of research paper on Computer and information sciences, author of scientific article — Tabarak allah Ali Mohamed, Salwa El-Sabban, Gamal Abdel Fadeel Mohamed Khalaf

Abstract In this paper, we incorporate the idea of waveband switching in Mixed Line Rates (MLR) network design to address the problem of dynamic traffic grooming in waveband switching networks by investigating a cost function which take the effect of call holding time on the time slot assignment process of in WDM–TDM. Use has been made of Markov model in order to predict the wavelength congestion. A routing algorithm is developed based on the Markov modeling. The results are compared with existing routing algorithms – Available Shortest Path (ASP) and Online Traffic Grooming Algorithm (OTGA). Validation results have shown that the performance of the proposed system is significantly improved in terms of bandwidth blocking ratio, network utilization as well as port saving due to wavebanding.

Academic research paper on topic "Multi-granularity grooming using timing information in optical networks with waveband and TDM switching"

Ain Shams Engineering Journal (2014) xxx, xxx-xxx

Ain Shams University Ain Shams Engineering Journal

www.elsevier.com/locate/asej www.sciencedirect.com

ELECTRICAL ENGINEERING

Multi-granularity grooming using timing information in optical networks with waveband and TDM switching

Tabarak allah Ali Mohamed *, Salwa El-Sabban, Gamal Abdel Fadeel Mohamed Khalaf

Helwan University, Elshorbagy - boulaq el- dakrour, Ahmed Ali Ismail Street, No. 28, Giza 12614, Egypt Received 11 June 2013; revised 26 November 2013; accepted 17 December 2013

KEYWORDS

Dynamic traffic grooming; Optical Time Slot Interchanger (OTSI); Holding time; Markov chain; Transient probability; Waveband switching (WBS)

Abstract In this paper, we incorporate the idea of waveband switching in Mixed Line Rates (MLR) network design to address the problem of dynamic traffic grooming in waveband switching networks by investigating a cost function which take the effect of call holding time on the time slot assignment process of in WDM-TDM. Use has been made of Markov model in order to predict the wavelength congestion. A routing algorithm is developed based on the Markov modeling. The results are compared with existing routing algorithms - Available Shortest Path (ASP) and Online Traffic Grooming Algorithm (OTGA). Validation results have shown that the performance of the proposed system is significantly improved in terms of bandwidth blocking ratio, network utilization as well as port saving due to wavebanding.

© 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

1. Introduction

Optical networks provide a transport infrastructure with very high capacity, thanks to wavelength-division-multiplexing (WDM) technology. The WDM technology divides the enormous fiber bandwidth into a large number of wavelengths and with current technologies; each fiber can have 100 or more wavelengths (each operating at 2.5 Gb/s or higher). In a wave-

* Corresponding author. Tel.: +20 01006793681. E-mail addresses: eng_tabarak.allah@hotmail.com (T.a.A Mohamed), salwa_alsabban@h-eng.helwan.edu.eg (S. El-Sabban), gam_hel@yahoo. com (G.A.F. Mohamed Khalaf).

Peer review under responsibility of Ain Shams University.

length-routed WDM network, a lightpath must be established between a pair of source and destination nodes before data can be transferred. A lightpath is an end-to-end optical connection which may traverse multiple fiber links and optical cross-connects (OXCs). However, Future telecommunication networks employing WDM technology, are expected to be heterogeneous and supporting a wide variety of traffic demands. Based on the nature of the demands, it may be convenient to set up lightpaths on these networks with a variety of bit rates. Traffic grooming refers to the problem of efficiently multiplexing a set of low-speed connection requests onto high-capacity channels and intelligently switching them at intermediate nodes. Traffic grooming problem in optical wavelength routing network has been extensively studied with the aims to minimize the number of optical-electronic-optical conversions (OEOs), or maximize the total number of users served in the optical networks. Thus, the network bandwidth utilization can be optimized. The traffic-grooming problem can be formulated as follows [1-10].

2090-4479 © 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University. http://dx.doi.org/10.1016/j.asej.2013.12.003

Given a network configuration and a set of connection requests with different bandwidth granularities, we need to determine how to set up lightpaths to satisfy the connection requests. Because of the sub-wavelength granularity of the requests, one or more connections can be multiplexed on the same lightpath using a multiplexing technique such as time division multiplexing technique (TDM) which divides the bandwidth's time domain into repeated time-slots of fixed bandwidth. Therefore, with TDM, multiple signals can share a given wavelength if they are non-overlapping in time [3,5-13]. The resulting multi-wavelength optical time division multiplexed network is referred to as WDM-TDM network. Hence, the available bandwidth on wavelengths can be utilized efficiently.

On another hand with the rapid advances in WDM technology, the tremendous growth in data traffic demands can be satisfied [14,15]. In practical dense wavelength division multiplexing (DWDM) and coarse wavelength division multiplexing (CWDM) technologies can divide the enormous fiber bandwidth into such a large quantity of wavelengths that each fiber can have hundred or more wavelengths. Hence, brought about a tremendous increase in the cost and size of electronic cross-connects or DXCs (e.g., OEO grooming switches). Optical (photonic) cross-connects (OXCs) that switch bypass traffic all-optically are useful in reducing the cost and size of the OEO grooming switches and to resolve the speed mismatch between the fast optical data network and electronic devices, where a network connection is maintained in the optical domain from source to destination. However, this breakthrough of WDM technology incurs a side effect. The more wavelengths a fiber link can offer, the more complex and expensive the control and management of OXCs become. Fortunately, the emergence of waveband switching (WBS) technique furnishes a solution to this problem [16-18]. With WBS technology, OXCs can efficiently aggregate a group of wavelengths into a waveband and transmit them as a unity as long as no wavelength dropping, addition, and extraction are required. Waveband switching (WBS) in conjunction with new multigranular optical cross-connects (or MG-OXCs) that can switch traffic at fiber, waveband and wavelength granularities [19-23], has been proposed to reduce this cost and complexity.

Lot of strategies for efficient lightpath routing in WDM networks have been proposed in these last years. We can classify these strategies in two main categories: alternate routing (AR) and dynamic routing (DR) [24]. In AR schemes [25-28], the route for the required connection is chosen among a set of predefined paths, which are usually assigned to each source/destination pair individually. Since the paths of such sets are usually determined priory by the network administrator, AR is not flexible enough to fully adapt to the variations in the network utilization. As for DR schemes [29,30], the connection route is dynamically determined according to the present state of the network.

Due to the evolution of services and applications over optical networks, traffic is becoming more dynamic. In a dynamic environment, a sequence of sub-wavelength requests arrives over time and each request has a random holding time. These requests need to be set up dynamically by determining a route across the network connecting the source to the destination and assigning it to a suitable time-slots on a suitable wavelength along the path.

In our work we consider all-optical WBS networks with proposed four-layer MG-OXC switching node architecture

to incorporate the idea of waveband switching in Mixed Line Rates (MLR) network design. It is envisioned that, a four-layer MG-OXC switching node architecture with the capability of associated TDM-time slot switching would significantly reduce the number of ports than that of the OXCs discussed in [5] moreover solving the traffic-diversity problems by using the time division multiplexing (TDM) technique effectively. To achieve that we exploit the knowledge of connection holding time to devise an efficient algorithm for dynamic traffic grooming of sub-wavelength requests in optical WDM mesh networks. A proper utilization of connection durations allows us to minimize the network resources used for each request, which implicitly attempts to minimize the overall blocking probability.

2. Related work

Much of the research work on routing and wavelength assignment (RWA) considers routing only at the wavelength level in wavelength routed networks (WRNs) [31,32]. Due to the nature of traffic demands, where the incoming requests need only sub-wavelength capacity, the mismatch between the required bandwidth of incoming request and the total available capacity of wavelength can be eliminated by which called traffic grooming. The problem of traffic grooming in optical networks is to determine how to efficiently route traffic demands and at the same time to combine lower-rate (sub-wavelength) connections onto a single wavelength. This problem took a lot of attention in most works [1-10] to achieve efficient utilization of the total available bandwidth of network resources (wavelengths).

On the other side, optical networks support the increasing data demands in telecommunication networks by utilizing many wavelengths and employing advanced transmission and switching technologies such as wavelength division multiplexing (WDM), dense wavelength division multiplexing (DWDM), coarse wavelength division multiplexing (CWDM) and optical cross-connects (OXCs), respectively. However, with the development of WDM networks and the increased number of wavelengths in WDM, cross-connects keep increasing the hardware cost and complexity at optical nodes such as reconfigurable optical add/drop multiplexers (ROAD-Ms) [33]. Hence, Recently research on multigranular waveband switching networks has received increasing attention [16,18,34-37]. Although wavelength routing is still fundamental to a WBS network, the challenging issues in WBS network are quite different from existing work on WRNs. For example, a common objective in designing a WRN is to reduce the number of wavelengths required or the number of wavelength hops used [31,32]. However, minimizing the number of wavelengths or wavelength hops [38] does not lead to minimization of the port count of the MG-OXCs. As the number of wavelengths is large, traditional OXCs that switch traffic only at the wavelength granularity can become huge (i.e., requiring a large number of wavelengths ports), resulting in increased cost and control complexity. This is led toward waveband switching (WBS) technique as a solution to this problem [16-18]. The main idea of WBS is to group several wavelengths together as a band, and switch the band using a single port whenever possible (e.g., as long as it carries only bypass or express traffic), and demultiplex it to switch the individual

wavelengths only when some traffic needs to be added/ dropped. As the bypass traffic accounts for up to 60% to 80% of the total traffic in the backbone, only a limited number of fibers and bands need to be demultiplexed into wavelengths. Thus, not only the size of wavelength cross-connects, but also the overall number of ports and complexity of the MG-OXCs can be reduced by using waveband switching [16,39-42]. At the same time, the increased switching ports and the saved cost by the waveband switching technique that can perform waveband grouping method to bind several lightpaths of wavelength level into one waveband to be switched by only one port [16], can be used for constructing survivable optical networks. Therefore, survivability in waveband switching optical networks has become a hot research [43]. In [37], the author discuss Regenerator Placement in Optical Networks with Impairment Constraints, where in an impairment-aware waveband network, a lightpath needs to be electronically regenerated before its signal to noise ratio reaches an unacceptable level. However, when a lightpath in a waveband needs to be regenerated, the entire waveband needs to be demultiplexed into wavelengths, resulting in additional wavelength ports at a node. Regenerator placement in a waveband network should be done so as to facilitate banding of lightpaths and to reduce the total cost of switch ports in the network. He formulate the regenerator placement problem in an impairment-constrained waveband network as an integer linear program (ILP), propose three heuristics and show that the performance of the proposed band-aware reachability graph heuristic yield solutions that are close to the ILP for small networks.

A categorization of WBS schemes can be constructed from a sequence of determined characteristics [44]. Generally, the following three are what most papers often consider:

• Number of bands in a fiber (denoted by B): the value of B may be fixed or quite different from each other.

• Number of wavelengths in a band (denoted by WB): the value WB of may be fixed or variable.

• Composition of a band: the set of wavelengths in a band can be predetermined or dynamically configured.

In [44], the categorization has been visualized as a tree as shown in Fig. 1. First, all WBS schemes are classified into

two categories, depending on the adaptability of the number of bands in a fiber. Similarly, each variation is further categorized according to whether the value of WB is fixed or not. For each variation at the second level (where the root has level zero), the criterion of the next-level classification is whether the set of wavelengths is predetermined or dynamically configured. In short, each path from the root to a node at the last level (a terminal node) corresponds to a unique WBS scheme. In our work, we concentrate on the simplest WBS scheme in which each fiber has a fixed number of bands B and each band has a fixed number of wavelengths WB with consecutive indices.

Waveband grouping strategies can be categorized into the following classes [45]:

• End-to-end grouping: as shown in Fig. 2, only lightpaths with the same source and destination can be grouped into a waveband.

• One-end grouping: this strategy groups only lightpaths belonging either to the source or to the destination into a waveband. In the former case, lightpaths aggregated at the source node can be de-multiplexed into wavelengths and dropped at any intermediate node. For the latter case, traffic with the same destination node is grouped at intermediate nodes along the routing path as shown in Fig. 3.

• Sub-path grouping: regardless of kind of nodes the source and destination are, lightpaths with a common sub-path can be aggregated, so that traffic can be added to and dropped from a waveband at arbitrary intermediate nodes as shown in Fig. 4.

Obviously, the third one is the most flexible strategy; however, it is the most complex one to develop as well. In order to exploit the benefits of WBS technology as much as possible, all discussions in this paper are based on the sub-path grouping strategy.

However, routing in WBS Networks contributes in port savings in the three-layer MG-OXC [16], wavelength routing is still fundamental to WBS networks as mentioned before, and due to the nature of the demands, most applications require only sub-wavelength capacities, the available bandwidth on a single wavelength far exceeds the capacity requirement of a typical connection request. For example, high

Figure 1 Waveband switching schemes.

Figure 2 End-to-end grouping strategy.

Figure 3 One-end grouping strategy.

Figure 4 Sub-path grouping.

definition television (HDTV) works well with just 20Mbps. As wavelengths are critical resources in WDM optical networks, the available bandwidth on wavelengths needs to be utilized efficiently. To overcome the disparity between the bandwidth required by connection requests and the available bandwidth on wavelengths, a technique called traffic grooming has been proposed [1-10].

3. Our contributions

Routing of connection requests based on the wavelength level has led to insufficient utilization of the available bandwidth. This is quite true especially where most of applications require only sub-bandwidth(s). This has led to the need of time division multiplexing using TDM switching capability for traffic

grooming. In this paper, we develop on the work presented in [5] in order to address this problem. Here we consider four-layer MG-OXC node architecture in order to utilize the wavebanding scheme with multi-rate optical networks. In this respect, we propose a new grooming algorithm in which holding time awareness is used in order to control the time slot assignment grooming in waveband switching in optical networks (WBS). In this respect, an estimate of the close-future congestion probability of network wavelengths is developed based on knowledge of the connection's durations. The estimation is, then, used to apply a holding-time-aware time-slot/ wavelength assignment in each band for on-line routing in a WDM-TDM mesh network. The proposed algorithm which we are developing is called, online multi-granularity grooming based on time-slot/wavelength congestion (MG-TGTSWC).

MG-TGTSWC not only performs traffic grooming and waveband switching together, but also solves the traffic-diversity problems effectively, especially in terms of port savings.

In particular, our approach is seen to outperform the existing dynamic routing algorithms which was done on time slot assignment and achieve a significantly better Blocking Probability due to holding time awareness of incoming requests and, at the same time, available bandwidth of network wavelengths has been efficiently utilized over which it takes wavelength to be the fundamental routing.

The rest of the paper is organized as follows. The four-layer node architecture and network modeling are introduced in Section 4. Section 5, provides an overview on the existing routing Algorithms for Incremental Traffic. In Section 6, holding time aware multi-granularity grooming in WBS optical networks is presented. Section 7, presents a statistical model for the Time-slot/wavelength congestion probability. This model is then, used to devise a computationally tractable, efficient algorithm called MG-TGTSWC for the dynamic routing problem. The findings in this paper are evaluated by numerical simulations in Section 8. Section 9 draws some conclusions.

4. Notations

4.1. Node architecture

Fig. 5, illustrates the Four-layer MG-OXC node architecture of a WDM-TDM switched mesh network. The entire node shows the architecture of a four-layer multigranular photonic cross-connect. The photonic cross-connect includes the three-layer MG-OXC described in [11] and added to it the fourth-layer including the optical time-slot interchanger (OTSI) layer[46], which consists of a TDM multiplexers/demultiplexer^). The OTSI layer includes TDM switching unit for traffic aggregation that allows for grooming of sub-wavelength traffic. The TDM switch is capable of arbitrary TDM time-slot interchanging as well as Wavelength-to-time slots (WTTS) demultiplexing and time slots-to-wavelength (TSTW) multiplexing.

As can be seen, the switch represents a node supporting M links of fiber (e1,e2,.. .,eM), each link is divided into fixed number of bands B, fixed number of WB wavelengths per band and each wavelength is divided into number of TS time-slots of fixed bandwidth (t1,t2,.. .,tTS).

Let X denotes the number of incoming fibers, Y the number of band cross-connect (BXC) ports from fiber to bands (FTB) demultiplexers, i.e., a 6 1 is the ratio of fibers (to the total number of fibers) that can be demultiplexed into bands using FTB ports. b 6 1 is the ratio of bands that can be demultiplexed to wavelengths using band to wavelengths (BTW) ports. And similarly, y 6 1 is the ratio of wavelengths that can be demultiplexed into time slots using WTTS ports. Still four-layer MG-OXC architecture is reconfigurable (hence, is flexible) in that any [aX] fibers can be demultiplexed into bands, any [pY of these bands can be demultiplexed into wavelengths and any of [yZ] these wavelengths can be demultiplexed into time slots simultaneously by appropriately configuring the MG-OXC. We show that even with limited reconfiguration (i.e., a <1, b <1 and y < 1), we can use an intelligent algorithm (MG-TGTSWC) for routing and time-slot/wavelength/ waveband assignments in order to, considerably, reduce the port count required to satisfy a given dynamic traffic requirements with acceptable request blocking probability while efficiently utilizing the available bandwidth of network wavelengths.

The total number of ports at such a reconfigurable, four-layer MG-OXC node can be calculated as in (Eq. (1)).

MG - OXC,

nIFour-layer MG-OXC

(1 + a)x X + Fadd/drop + (1 + b)x Y

^Baddj drop

+ (1 + y)xZ +

^Waddj drop

y x Z x TS + TSaddj drop

If we consider single-fiber system and by letting M be the node degree, then, we have,

X — M, Y — [a x M x B], Z =[b x Y x Wb] = [p x a x M x B x WB],

Recall to three-layer MG-OXC discussed in [16,41,42,47]. The total number of ports at such a reconfigurable, three-layer MG-OXC node can be calculated as given by (Eq. (2)).

MG - OXC,

n I Three-layer.MG-OXC

(1 + a)x X +

Faddj drop ^

b x Y x Wb + Wadd/drop

(1 + b)x Y + BaM/drop+

From (Eq. (1)) and (Eq. (2)), we show that, the number of ports in the switched node increased to be a Compatible with the heterogeneous telecommunication networks and can support a wide variety of traffic demands over that supported by the three-layer MG-OXC described in [16,41,42,47] by a factor T1 as shown in (Eq. (3)) which introduced due to TDM switching layer supported by the four layer.

T1 = MG — OXC„\Four_IayerMG_oxc — MG — OXC„\Three_IayerMG_oxc

T1 —

(1 + a)x X + Fadd/drop + (1 + b)x Y + Baddjdrop + (1 + y)x b x Y x Wb + Waddjdrop +y x b x Y x Wb x TS + TSaddjdrop

(1 + a)x X + Fa

addjdrop

(1 + b)x Y+

addjdrop

b x Y x WB + WL

addjdrop

T — y x b x Y x Wb(1 + TS) + TSaddjdrop

T1 — a x b x y x M x B x Wb(1 + TS) + TSaddjdrop

T ffi a x b x y x WBTS

Figure 5 MG-OXC node architecture for sub-wavelength traffic grooming.

Note that, when a =1, b = 1, c = 1, there is no limitations on the number of fibers/bands that can be multiplexed/demultiplexed and, hence, the blocking of a lightpath request can only be due to unavailability of the bandwidth that can accommodates the requested demands as in the ordinary-OXC network with TDM switching capability discussed in [5]. For an ordin-ary-OXC, that only switches individual wavelengths with the capability of time slots interchanging using OTSI to support WDM-TDM networks, the number of ports at node n is given by (Eq. (4)).

[M X B X Wb X TS + TSadd/drop]

Accordingly, if we ignore TSadd/drop, (which are common to both the four-layer reconfigurable MG-OXC and the ordin-ary-OXC), also ignore Fadd/drop and Badd/drop, the ratio of the port count in the four -layer MG-OXC to the port count in an ordinary-OXC discussed in [1,5,34], denoted by T in (Eq. (5)).

(1 + a) M +(1 + p)x a X M X B +(1 + y)X b X a X M X B X W+ y X b X a X M X B X W X TS

\M X B X W X TS]

T ffi a X b X y +

(1 + y)X a X b

and time slots respectively (otherwise, the blocking probability is too high). However, we can limit the value of b to be less than 1 by allowing only a limited number of bands (i.e., [bY]) to be demultiplexed into wavelengths simultaneously.

4.2. Network model

The physical topology of a WDM-TDM mesh network can be represented by an undirected graph G = (V, E) consisting of | V| = n nodes and |E| = M links interconnecting the nodes. Each link in the physical topology is bidirectional and is modeled as a pair of unidirectional link. Each link is divided into fixed number of B bands, a fixed number of WB wavelengths per band and each wavelength is divided into number of repeated time-slots (TS) of fixed bandwidth (ti,t2,.. .,tTS). According to wavebanding, we model WBS optical network [16] as shown in Fig. 6, where the physical topology (an undirected graph) as depicted in Fig. 6a, is divided into B-sub-undi-rected graph, called B-band graph Gb' — (Vb', Eb') as indicated in Fig. 6b. The nodes in each band graph b' e B correspond to the nodes in the physical network topology, while the links between the nodes correspond to the existence of that band between the nodes. We denote the set of existing sub-(5) wavelength connections on any wavelength w on any band

Therefore, in order to reduce the port count by using MG-OXCs instead of ordinary-OXCs, the values of a, b and c need to be constrained so as to ensure that T < 1. For a single-fiber systems, it is necessary to set a = 1 and c = 1 in order to allow any fiber and wavelength to be demultiplexed to bands

b' e B in the network at any time by,

bb —

| (V'w'>b', dw'b', •b', t'f, tf 'b') }

where the quintuple si;w ;b ; di;w ;b ; li;w ;b ; taw ;b ; thw ;b specifies,

respectively, the source node, the destination node, the route,

OXCn —

(b) B—band graigh

0,={Vb;E,)

Figure 6 Explanation of network model.

the arrival time and the holding time for the ith connection on a wavelength w' belonging to a given band b'. We associate a wavelength utilization level descriptor vw b' to each wavelength w' belonging to a certain band b' e B in each link (u, v) 2 Eb' in the network. Therefore, the occupation of time-slots on a wavelength can be represented as an integer set {vwb\8w', 0 6 vwb 6 TSg. Using vw,b', the on-line traffic grooming objective is to find path(s) with minimum cost and bandwidth PW,b on wavelength(s) w' on a band b' e B between a source node si,w,b' to its destination d'w,b at a given arrival time t'ffor a duration t'hW,b and, at the same time, with maximum sum of overlap length OVL (number of links in common with all existing).

The objective is to maximize the network throughput such that the established requests must not be interrupted while saving the ports in order to reduce the complexity of switching node.

5. Dynamic routing algorithms

In this section, an overview on dynamic routing approaches in WBS with TDM switched optical networks is presented. Using the above network model, we assign the incoming sub-wavelength request to number of time slots as needed. In this respect, we assume that a wavelength is divided into 16 timeslots; each has a fixed bandwidth equivalent to one OC-3 channel. Therefore, the total available bandwidth per-wavelength X is equivalent to an OC-48 channel, hence, X =16 OC-3s.

In general terms, only links with sufficient bandwidth capacities to accommodate the requests are considered and the Dijkstra's algorithm is adopted in order to find the least-cost, Clw ;b , path between each source-destination nodes in each band graph b' e B. from CW,b we get the time slot assignment in a certain w belonging to a band b e B which have minimum cost.

cW,b' _

Cu,v —

RBi 6 RC(u, v, W Otherwise

,b' ) 6 X

Such that CW,b — X , C?' Minimized

l Z-^(u,v)el u,v

where RC(u, v, w',b'), the residual capacity of w' on link (u, v) belong to b -band graph, Cmw: vb refers to Cost of using this wavelength w' on the link (u, v) of b' -band graph and C,b is the total cost of the route between the source and the destination nodes in b -band graph. When two or more paths are having equal costs on the b -band graph, the one with minimum hop count is selected. If two paths have the same hop count, then the tie is broken by using the first-fit wavelength assignment policy [48,49]. For the purpose of completion, the following cost function model [2] is outlined.

Let iu v represents the total available bandwidth on a given link (u, v) 2 Eb'. Therefore, we have

ft, v — Wf x X 8(u, v) 2 E,

where WF is the total number of wavelengths carried by each link (u,v) e E in the physical topology. For convenience, the requested bandwidth RBi is normalized to the total available bandwidth on a link (u,v) e E. Therefore,

RB(u, v) — RRBi

And the load on a link (u,v) e E after considering a request k is defined as,

C — E RBj(u, v) j — 1 (u, v) 2 Pj

Now, let Rwb (u, v) be the residual capacity on wavelength w' on link (u, v) 2 Eb' after considering the first K requests is given by,

R - i vwwLl.

By checking that RC(u,v,w',b') the residual capacity of w' on link (u, v) 2 Eb' in terms of the number of OC-3 channel, the

Cost C Vb of using the number of time-slots (OC-3 channels) requested for a connection i on a wavelength w' belong to b'-band graph is represented by:

a1'.- (aRB'(u• v) - 1) RC(u,v, w' ,b') — X

cwt = { a'«.-(aRB,(u,v)-1)

bRw b'(

RBi 6 RC(u, v,W, b' ) < X Otherwise

where a and b are constant > 1. Later in this paper, we shall present our Time-slot/wavelength cost assignment that evaluates Future Wavelength Utilization FWUw b probability for each b -band graph in WBS optical networks based on the results of Markov modeling of time-slots occupation on wavelength w' belong to b' -band graph, as described in (Eq. (19)).

6. Holding time aware multi-granularity grooming in WBS optical networks

Due to the nature of dynamic traffic, connections are established and released randomly. Hence, wavelength congestion level changes during the holding time of incoming connections [5,42,48-51]. This means that, we can exploit the information about the connection departure events, which is retrievable from the knowledge of the connection's holding time. Hence, we could modify the time-slot/wavelength cost assignment in each band graph b' e B to capture the future degree of utilization of a given wavelength belonging to this band in terms of requested number of time slots as well as the estimated occupation time. More specifically, we can determine the residual lifetime h;w b' of an existing connection i on a wavelength w' belonging to a band b by the largest ending time of the connection as follows,

hi,w', b

ff," + thW,b - Ta if (ta

i w b i w b

a + th

-t'hW ,b 6 Ta + Th)

otherwise

where t^,b, t'hw, and Ta, Th are the pairs ''arrival time'', ''holding time'' of the existing connections on wavelength w' belonging to a certain band b'. We introduce the symbols

vw', b' (Dsk,w',b') and Cw'Z (Dsk,w' , b'), which expreSS the values of

wavelength utilization vw,b' in band b' and the cost of using wavelength w' in a link (u , v) e Eb' in b' - band graph (respectively), in the time interval Dsk,w which is obtained according to the values of the ending life time of an existing connections as given by (Eq. (13)) above.

The values of hiw, ,b' 's are then ordered as hiw',b' 6 hi+1, w' , b', i — 1,2 ,..., \L\. As a consequence, , b' — { ,w, b ,

s1, w' , b', ... , s\L\ w b } — {0 , h

,w' , b', h2.w' , b', ... , h\L\, w' ,b'} indicate the

departure events in the interval Th of incoming connection re-

quest on a wavelength w' on a band b' and Dsk

' sk, w', b'"

expresses the time interval between two departures

on a wavelength w on a band b . Wavelength utilization ; b (Ask; wb) and the associated cost C^'b (Ask; w; b') will be updated according to the k-th connection's departure. In other words, we have divided the interval Th of incoming connection request into a series of time intervals Asw' ; b' for each band b' e B which expresses the distance between two departures for each wavelength w belonging to a certain band b .

7. Occupation time estimation

In this section, we use the time-dependent Markov chain model [5] in order to estimate the future occupation of the requested number of time-slots on a given wavelength w belonging to a certain band b in each band graph where the duration of existing connections are represented as shown in Fig. 7.

Let XX={XX(t):t P 0} be the homogeneous continuous-time Markov chain describing the time-slot occupation process on a given wavelength w belonging to a certain band b , with transition matrix Qw'b. Let q™'b be the (i, j)-th element of Qw'b, and qw'' b' — Y,^'b', be the rate of state i.

Now, let ZZ = {ZZn: n = 0,1,...} be a discrete time version of the Markov chain with the same state space but with transition probability matrix Pw'vb' — I + Qw' 'b'b' for each wavelength w' on each link (u ' v) 2 Eb' in a b' -band graph, where K

v, b' — maxi{qw , }.

ku,v,b' Kw' b

ku,v,b'

u,v,b Kw' b

Kw' b'

Kw' b'

Assume now that, N = {N(t): t P 0} is a Poisson process with rate K independent of ZZ. Then, if the time between transitions for the chain ZZ is exponentially distributed with rate Kw'b, then the residence time spent in a visit to state i, is exponential with mean 1 /qw,b. Since the total residence time in i is identical in both of the continuous and discrete processes as well as the probability of moving from i to j. We may consider that XX and ZZ to be equivalent processes.

Now, let nw' , b' (t) be the vector such that the j-th element equals to the probability that XX is in state (time-slot) j at time

Figure 8 Example on transition probability analysis of a wavelength w' belonging to b'-band graph.

', b '

k-1, w', b'

t, given an initial distribution of the states. After n transitions, 7.1. Time slot mean transient probability

ZZ will be in state j with probability vW, b (n), where vj,b (n) is the j-th entry of the vector vw' ,b (n) — vw ,b (0)PJ, b and vw' b (0) is the initial state probability vector. Independent of the number of transitions in the interval (0, t), we obtain

nw' ,b' (t) —£ 1

A, b't (Kw' , b't)n

e Aw , y

Vw',b (n)

where Pnw b is the TS's transition probability matrix on wavelength w' belonging to a band b'. If we truncate (Eq. (14)) for a given values of N-TS, the error e(N) of any entry of the vector nw'; b' (t) is given by:

e(N) 6 1 - £e-

A_, „ t (AW,b't)

As can be seen, for a relatively large N, the truncation error can be neglected [25].

In general, the mean transient probability in a given state can be obtained if we consider the time interval asw,b'. Hence, the mean values of each element in the vector, nw ; b (t) is given by,

nW' , b' (Dsw' ,b' ) —

■>Asw b' ^n

Aw' b't <A»' bt)n vw',b'

ne-Aw'

( n ) dt

vw', b' (n) ',=0 n!

1M r ■i J b

-AW' bt

(Aw',b't)ndt

1 v»' , b'(n)

!(n)(1 - e w'

Aw' b' Asw'

i—0 (n-i)i

(Eq. (16)) can easily be computed recursively. Details are skipped for the sake of brevity.

7.2. Wavelength transient-state expected value

Figure 9 Experimental telecommunications network topology.

Since Ejp"',b (t) = 1 at each time instant t, and that the n;' b (Atw, b ) defines the mean transient probability of the j-th time slot during the time interval Asw' , b', we can express the expected value of asw b' in a wavelength w' belonging to band b' e B by (Eq. (17)): ,

ES)nw' ,b' (Asw ,b' )*j

w b j— 0 j w b

Ew (Asw' , b')—-Ts

7.3. Transient probability during a connection's holding-time

Now we can define the expected-mean occupation of a time slots in a given wavelength w' belonging to each band b' e B,

Figure 10 Bandwidth blocking ratio versus the increased factor (T1) of the port count with changing b at load 550 (in Erlange).

' ,b '

over a time interval Th starting from the arrival time Ta of an incoming connection. For sake of illustrations, we focus on the example shown in Fig. 8, where we draw the time persistence of two existing connections r1 and r2, each of which reserves one time-slot on a wavelength w'(TS = 4) belonging to b -band graph, while connection r3 is requesting one time-slot. Let us suppose that ku v b' is the mean value of the connection arrival rate to link (u ' v) 2 Eb' and 1/i its mean holding time. If r3 arrives to the network with holding time Th = 20, rx has to linger on wavelength w other 10 time units.

Therefore, its lifetime on that wavelength will be set to h1wbb' — 10. As for r2, even if r2 has to be operated other 30 time units, in our analysis, its lifetime on the same wavelength w' is bounded to h2ww b' — 20 according to (Eq. (13)) Thus, the holding time Th is split into two time intervals As1 w b and As2wbb' (in the present example). Let us set s0 w' b' — Ta, for each time interval Ask w b we compute: an auxiliary transition probability matrix Puw vb k with initial state probability vector vf 'b' (0), the final state probability vector nw''b' (Ask w b') and the expected value E^''b' (Asky'b'), from which the auxiliary probability matrix Pbuw vb k of the k-th time interval is defined as PwJ'k — Ik + Qi'b'/Kk, where 4 and Qwk''b' are given by the Hadamard product of the following matrices:

Bw' ,b' _

Qw,b ■ H« îk — I ■ H«

where Hk functions as a filter function: Hk is composed by 0s or 1s: the (i, j)-th element will be set to 1 if and only if i and j are strictly greater than the minimum number of time-slots in a certain wavelength, certainly occupied in the time interval Askybb', otherwise it will be set to 0. Let qjj 'b be the (i, j)-th element of Qw'b', and qk'w' ' b' — Y.jkjw''b', designates the exponential rate out of state i. Moreover, Aky b' — max,-{qk'w 'b }. The auxiliary probability matrix Puw vb k is utilized in place of Puw vb to obtain the truncated Markov chain corresponding to the minimum number of time slots reserved for the existing connections that are certainly supported by the wavelength during the time interval Ask w b as follows:

• As, w' b' (From time 0 to 10): the minimum number of occupied time-slot in a wavelength w belonging to a band b e B is 3 (we assume that the incoming connection r3 is routed on the same wavelength w' on the same link (u' v) 2 Eb' of a b' -band graph. Therefore,

PwJ' ,1(As1.w' ,b ) —

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 -

ku,v,b' K,v,y

^ — =41

where A!yfi' — maxfk^ v,b''4l}

• At2.w'b' (From time 10 to 20): the minimum number of occupied time-slots is 2, since r1 departs from wavelength w and leaves the network at time 10. Therefore,

Table 1 Initial and final vectors during As1 y b< AND As2'w y.

0 12 3 4

■w,b (0) w (s1 , w , b)

nw,b' (S2,w' , b)

0 nw' ,b' (10)

(10) b (10) (20)

nw b (20)

0 0 0 0 0

0 0 0 0 0

0 0 1 _ v,"' K,vb 0

0 0 1 31+ku,v.b'

B2 K 2 B2

0 0 0 1 - J1

- B2 K2

where A2'w^ — max{3i + ku vb''4i}. In Table 1 below, we report the transient state probabilities of the initial and final vectors during the time intervals Atj w' 'b' and As2 'wbb'.

Note that, since connection r1 departs (deterministically) from the wavelength w belonging to a band b eB and leaves the network at time Tj w ^ — 10, the initial vector V2w b of the interval At2w is obtained by a cyclic-left-unitary shift of the previous final state vector nw 'b (10). Then, by (Eq. (14)) and (Eq. (17)), we can compute the final state probability nw' ' b' (Tk ' w ' b') and the expected value E ' b (Ask) for the wavelength w belonging to a band b e B for each time interval Ask' w' b'. Finally, we can define the close Future Wavelength Utilization FWUw 'b of wavelength w' belonging to a band b' e B as the average of the expected value Ew 'b (askwwbb') within the holding time of the incoming connection Th:

FWUw' ,b' = ^

\L\ K—1

Ew' , b' (Ask,w',b' )

7.4. The Propose MG-TGTSWC approach

In this section, we illustrate our dynamic traffic grooming approach in WBS networks associated with TDM switching capability. Given that there is no wavelength or waveband conversion in the MG-OXCs, we model a WBS network as shown in Fig. 6a using band graphs (one for each band) as in Fig. 6b. The routing algorithm is executed for each band graph iteratively on per wavelength w belonging to a certain band b e B for each band graph. The aim is to minimize the request blocking probability by determining the best possible time slot and wavelength assignments over the best available route for a given request in each band graph. The way this is achieved is based on the time-dependent model which estimates the future occupation FWUw b of the requested time slots (TS) on each wavelength w in a certain band b given the duration of connection.

In the following, the cost of using a number of time slots (TS) on a wavelength w' on a given link (u ' v) 2 Eb' on each a band graph b e B for a connection request Th is given by ' ' Th):

Since the load on each link (u ' v) 2 Eb' is described by

(Eq. (10))

Cw b Cu, v

C = £ j = 1 RBj(u ,v) ,

(m , v) 2 Pj

when a new connection request i arrives, we check RC(u, v, w', b') the residual capacity of w' on link (u , v) 2 Eb' in terms of the number of OC-3 channels and then assign the cost of using the requested number of time slots (TS) on each wavelength w' on each link (u , v) 2 Eb' of a band graph b' 2 B as follows::

/"W ; b

(Th) =

aFWU'-"' + ß{lkJb + 1) Otherwise

RC(u; v , w') < RBi

Such that

= ^CWf (Th) Minimized

Intuitively, in order to satisfy a new request demand with as few additional ports as possible, we should use existing waveband paths as much as possible in order to reduce the cost. Hence, the routing is computed over a collapsed topology with modified link costs favoring existing ''waveband-path links''. To achieve a balance, we set the weight of using a number of time slot in a certain wavelength belonging to a certain band CFw'b to be OVL/Cf;b', where OVL is the sum of overlap length (number of links in common with all existing lightpaths) in band b and Clw b is the possible minimum route cost between each source and destination nodes using a certain wavelength w belonging to a certain band b . Algorithm MG-TGTSWC chooses a path that has the maximum weight CFw b , to route the new request demand and assign the requested time slot to a wavelength w and a band b to it.

To evaluate the performance of the proposed algorithm, we conducted experiments on the mesh network shown in Fig. 9, which consists of 24 nodes and 43-fiber links. Each fiber link is

divided into 8 bands, each band carries 2 wavelengths and each wavelength is divided into 16 time-slots. The bandwidth available on each time-slot is one OC-3. All the nodes in the network have the architecture shown in Fig. 5. We further assume that no wavelength or waveband conversion capability imposed. The bandwidth required by connection requests is uniformly distributed between one OC-3 and sixteen OC-3s.

8. Numerical validations

In this section, we discuss:

1. The utilization of the available network wavelength in both three-layer MG-OXC [16,41,42,47] and the proposed four-layer MG-OXC (with TDM switching capability). While using the four-layer MG-OXC with TDM switching capability have increased the number of nodes over that with the three-layer MG-OXC, we can, however, incorporate the idea of wavebanding in MLR network design and thus solve the traffic-diversity and support various traffic demands. On the other hand, the proposed four-layer node architecture have achieved lower blocking probability and hence provided higher network utilization due to the added TDM switching fabric which have led to efficient use of the available bandwidth of the network. For a single-fiber systems, it is necessary to set a = 1 and C = 1 In order to allow any fiber and wavelength to be demultiplexed to bands and time slots respectively (otherwise, the blocking probability is too high). However, we can limit the value of b to be less than 1 by allowing only a limited number of bands (i.e., [bY]) to be demultiplexed into wavelengths simultaneously. Here we illustrate how the bandwidth blocking ratio resulted from both node architectures and how it is affected with changing b (i.e., the ratio of bands that can be demultiplexed/multiplexed). It represents the percentage of the amount of blocked traffic over the total amount of

■a 3

250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 NO. of requested connections (in Erlange)

Figure 11 Bandwidth blocking ratio versus load at with changing b.

ARTICLE IN PRESS

12 T.a.A. Mohamed et al.

NO. of requested connections (in Erlange)

Figure 12 Average network utilization versus load at with changing b.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.3 0.9 1

Ratio:T

Figure 13 Blocking probability versus the ratio (T) of the port count in a four-layer MG-OXC at load 550 (in Erlange).

bandwidth required by all the connection requests during the entire simulation period. To achieve this, we use two routing algorithms: Maximum Overlap Ratio (MOR) in case three-layer MG-OXC as described in details in [16] and the ordinary Available Shortest Path (ASP) in the four-layer MG-OXC case. From Fig. 10, we can see that the total bandwidth blocking ratio is reduced as a result of the use of four-layer MG-OXC node architecture. This reduction is due to the added TDM switching capability with increased ports by factor 12.8 (increased factor T1) at the X-axis as cleared in (Eq. (3)), also we can notice the effect of changing b on with constant value of a and y where after b = 0.4 there is no effect the bandwidth blocking ratio, hence we do not need over than [bY] to reduce the bandwidth blocking ratio. This saving in ports resulted due to wavebanding. When a =1, b = 1, y = 1 (i.e. there is no limitations on the number of fibers/ bands/wavelengths that can be multiplexed/demultiplexed) the blocking of a lightpath request can only be due to unavailability of the network resources (wavelengths in case three-layer MG-OXC) and the bandwidth of the wavelength that can accommodates the requested demands (time-slots) in case four-layer MG-OXC). Using four-layer MG-OXC have lower blocking probability because almost all requests need only sub-wavelength capacities and hence by TDM capability in four-layer MG-OXC, we can established more requests than using three-layer MG-OXC, and it is clear from Figs. 11 and 12 which illustrate the total of bandwidth blocking ratio and its impacts on average network utilization during various load with changing values of b (respectively). The average network utilization is determined as follows. Consider a connection request i between nodes st and di with capacity requirement RBi. Let the distance between them be Di. Now, if connection request i is to be established, then irrespective of the routing algorithm used, the minimum capacity required in the network is RBi x Di. This is called the effective capacity requirement of the request. Depending on the routing algorithm employed,

the number of hops taken by it to establish the connection request may be greater than Dt. Denote by ENC, the effective network capacity utilized at any instant of time. ENC is defined as the sum of the effective capacity requirement of all the connection requests that are active at that instant. The total network capacity is defined as M x B x | W| x X. The network utilization is, then, determined as the ratio of the effective network capacity utilized to the total network capac-

x. when b is changed from b = 1 to b = 0.5 and

MxBx|W|xQ'

b = 0.1 the request blocking probability increases because it now due to insufficient number of free ports in BXC layer that can demultiplex bands, and/or unavailability of the network resources from Figs. 11 and 12, we see that using four-layer MG-OXC achieve lower bandwidth blocking ratio and thus higher average network utilization.

2. Using four-layer node architecture with TDM switching capability, we compare the performance of (MG-TGTSWC) which take into account holding time of incoming request with other existing routing algorithms - ASP (Available Shortest Path) and OTGA (Online Traffic Grooming Algorithm) [2], Results have indicated that, the four-layer MG-OXC architecture with the capability of TDM switching is more suitable with fully dynamic traffic with a holding time aware scheme. Its occupation awareness has improved the performance over the existing routing algorithms. The metrics used to measure the performance of the algorithms are as follows,

(i) Blocking probability with port savings: As can be seen from Fig. 13, the proposed MG-TGTSWC achieves superior blocking probabilities over that of OTAG and ASP. On the other hand, we note that, when b = 0.4 (i.e. Ratio: T = 0.45 at the X-axis according to (Eq. (5)) MG-TGTSWC achieves the lowest blocking probability. Increasing b to greater values than 0.4 does not help in reducing the blocking probability any further

250 275 300 325 350 375 400 425 450 475 500 NO. of requested connections (in Erlange)

525 550 575 600

Figure 14 Bandwidth blocking ratio versus load by different routing algorithms at (b = 0.4, and T = 0.45).

ASP ■ OTGA A MG-TGTSWC

250 275 300 325 350 375 400 425 450 475 500 525 55D 575 600 NO. of requested connections (in Erlange)

Figure 15 Average network utilization by different routing algorithms at (b = 0.4 and T = 0.45).

because now blocking occurs only due to limited wavelength resources and not due to limited reconfiguration flexibility (e.g., ports).

(ii) Bandwidth blocking ratio: Fig. 14 compares the bandwidth blocking ratio for different routing algorithms using four-layer node architecture with TDM switching capability at (b = 0.4 and T = 0.45). The percentage of total bandwidth blocked by MG-TGTSWC is lower than that of the other three heuristics at different loads. This simply means that the MG-TGTSWC provides higher network throughput, and thus offers better performance.

(iii) Average Network utilization: by determining the average network utilization as explained previously. Fig. 15, shows that MG-TGTSW outperforms the other existing routing algorithms in terms of the network utilization by mean of routing the requests in terms of the number of time-slot as requested.

9. Summary

In this paper, on-line traffic grooming in WBS optical networks with TDM switching with no wavelength or waveband conversion capability in the four-layer MG-OXCs. While using the four-layer MG-OXC with TDM switching capability have increased the number of nodes over that with the three-layer MG-OXC, we can, however, incorporate the idea of wavebanding in MLR network design and thus solve the traffic-diversity and support various traffic demands. On the other hand, the proposed four-layer node architecture have achieved lower blocking probability and hence provided higher network utilization due to the added TDM switching fabric which have

led to efficient use of the available bandwidth of the network. a novel, intelligent approach to dynamic routing based on knowledge of the connection's-holding time is formulated and its performance is numerically validated. Results are compared with existing routing algorithms. The following observations conclude the validation results:

(i) Port savings due to wavebanding has been achieved Fig. 13 (T = 0.45 < 1 as (Eq. (5)).

(ii) Better bandwidth blocking probability.

(iii) Higher network utilization.

As a result, we claim that the proposed algorithm outperforms the existing ASP and OTGA algorithms and, hence, is qualified for practical applications.

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Tabarak Allah Ali Mohamed received the B. Sc. with grade Very Good (Honor) in Communications & Electronics Engineering from Faculty of Engineering, at Helwan, Helwan University, Cairo, Egypt, in 2007. She achieved 7th position on her intake College. Graduation Project Proactive Secure Multiparty Computations, with grade Excellent. In 2008 she received a preliminary Masters from Faculty of Engineering, at Helwan, Helwan University, Cairo, Egypt with Point of research: Optical Networks Based On WDM Technology with grade Very Good from 2008 till now she worked network engineering in judicial information center - ministry of justice, Cairo, Egypt.

Salwa El-Sabban obtained her B.Sc., and M.Sc. from the Faculty of Eng., Ain Shams University. From 1987 to 1996, she worked in the software development and marketing at Kolaly Engineering. She received her Ph.D. degree in Optoelectronics, from the INPG (Institut National Polytechnique de Grenoble) France in 2001. She is Assistant Professor at the Dept. of Electronics, Communication, and Computer Eng., in the Faculty of Eng., Helwan University since 2006. Her current interests include Integrated Optics, Optical Communication Systems, Tunable Laser, and Optical Filters. Dr. Salwa El-Sabban is a member in IEEE and SPIE. She is an author and co-author of one textbook and several international publications.

Gamal Abdel Fadeel Mohamed Khalaf received the B.Sc. and M.Sc in Communications Engineering from Faculty of Engineering, Helwan University, Cairo, Egypt, in 1977 and 1983, respectively. Received the Ph.D. in Computer Communication Networks, from Imperial College of Science, Technology and Medicine, London University, London, in October, 1990. He worked Lecturer and Assistant Prof. at Communications & Electronics Department, Faculty of Engineering, at Helwan, Cairo, from 1992-1999 and from 1999-2008, respectively. Head of Electronics, Communications & Computer Department, Faculty of Engineering, at Helwan, Cairo, 2008-2011. Professor of Computer Network Communications, at Communications & Electronics Department, Faculty of Engineering, at Helwan, Cairo, 2011-Now.