A novel node architecture for optical networks: Modeling, analysis and performance evaluation

Computer Communications 30 (2007) 999–1014 www.elsevier.com/locate/comcom

A novel node architecture for optical networks: Modeling, analysis and performance evaluation A. Lazzez, Y. Khlifi, S. Guemara El Fatmi, N. Boudriga *, M.S. Obaidat Engineering School of Telecommunication, Technopark, Ariana, Tunisia Available online 15 September 2006

Abstract Optical packet and burst switching technologies represent promising solutions for the next generation Internet backbone. Contention resolution and QoS provision, however, constitute the critical issues in the development of services using these technologies. In this paper, we propose a node architecture suitable for optical packet and burst switching that allows a prioritized buffering mechanism for contention resolution and QoS support. Our proposal is accompanied by a signaling protocol for packet-based traffic handling. We also develop a theoretical model for evaluating its performance based on a new conservation law and a queuing network model. Finally, a simulation study is performed to validate the proposed schemes.  2006 Elsevier B.V. All rights reserved. Keywords: Optical networking; Node architecture; Performance analysis and evaluation; Optical burst switching; Optical packet switching; Quality of service (QoS)

1. Introduction A large part of the existing telecommunication networks are SDH-based and have electronic circuit switched transport core. Works on automated switched optical network and generalized multi-protocol label switching have taken place within IETF and ITU to improve network performance [1]. Resulting optical circuit switched (OCS) networks can offer explicit transport guarantees since circuit establishments are confirmed and can provide more flexibility than the traditional solutions. However, high endto-end delays can be generated and the access to the optical bandwidth is still provided at a fiber/wavelength granularity. Since the Internet growth requires that future technologies must be able to serve at a packet level, OCS transport seems to be not highly appropriate. It lacks flexibility and requires an over-dimensioning of the number of connections and the bandwidth reservation of each connection [2].

*

Corresponding author. Tel.: + 216 98 645073; fax: + 216 71 856829. E-mail address: [email protected] (N. Boudriga).

0140-3664/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2006.08.023

Optical packet switching (OPS) [2,3] and optical burst switching (OBS) [2–4] seem to offer promising solutions because they can reduce delays and improve the utilization of the network resources. Unfortunately, the current state of development of these technologies cannot offer explicit transfer guarantees like those imposed by constraining QoS parameters, nor do they provide a suitable contention resolution. In a previous work [5], we have introduced a new architecture that can handle optical burst switching and enable better QoS support; therefore it has resolved the aforementioned shortcomings. In this architecture, we have considered the provision of differentiated and optimized services to IP packets. A prioritized optical buffering technique has been proposed for contention resolution and QoS support over an OBS network based on the proposed architecture. The proposed architecture adopts a slotted (or synchronous) optical packet and burst switching, which is easier to build and operate, and which may provide better performances than unslotted transmission [6–8]. In a synchronous OPS/OBS network, time is slotted, and the switch fabric at each individual node can only be reconfigured at

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the beginning of a time slot. In a slotted OPS/OBS network, all packets have a fixed-size equal to a time slot duration, and a data burst length is equal to some multiple of time slot durations [6–9]. In this work, we have mainly addressed the basics for a theoretical model for the performance evaluation of the novel architecture based on a new conservation law [12] and a queuing network model in order to provide an efficient mathematical analysis. Reference [11] also provides numerical results that validate the efficiency of the developed model. The work presented in this paper contains a synthesis of the work presented in [5,11] and extends the results achieved about the novel optical node architecture. It particularly develops the optical node synchronization, and contention resolution techniques processing. It presents a complete analytic model of the node architecture and realizes simulation results that show the impact of the main input parameters on the performance of the proposed architecture. Moreover, it confirms the results of the developed analytic model. The design and engineering of this proposed architecture have required the introduction of some new concepts such as the virtual optical circuit (VOC) and optical segment. The architecture has also required the definition of an ATM-like signaling protocol for packet-based traffic handling, as well as the use of the JET-like protocol that was previously proposed for bursts-based traffic signaling [10]. Models and experiments have been also needed to evaluate the performance of the proposed architecture and study its features. The remaining part of this paper is organized as follows. Section 2 presents the major components of the proposed architecture and their functions. It also details the synchro-

nization aspect and explains how the node performs packet and burst switching. Section 3 presents the signaling protocols used to handle packet-based and burst-based traffic. Section 4 presents the proposed QoS-based contention resolution mechanism. It also presents the contention resolution technique processing. Section 5 presents the developed analytical model, as well as its analysis technique. We also justify the coherence of a new conservation law used for the model analysis. Section 6 presents a simulation model and validates the performance model through the evolution of two parameters: packet loss and packet blocking. It also compares analytic results to the results obtained from simulation. Section 7 concludes the paper. 2. Node architecture The architecture that we propose for optical nodes is depicted in Fig. 1. The node is composed of N input ports and N output ports. Each channel can handle x wavelengths using a set of multiplexers and demultiplexers. Wavelengths are used either for signaling or traffic transport. The main components of the node architecture are: (a) a switch fabric unit, (b) a waiting unit, (c) a switch control unit, (d) an input processing unit and (e) an output processing unit. These components are useful for performing an effective packet and burst switching. The following subsection details the main functions of these units. 2.1. Optical node components 2.1.1. Switch fabric unit (SFU) The SFU carries input traffic units (i.e., packet or data segment) to the intended output channel or to an appropriately selected fiber delay line (FDL), in case of

Fig. 1. Optical node architecture.

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output port contention. Two main schemes of switch architectures can be proposed for optical packet and burst switching: space switches [13] and wavelength-routing switches [14]. The first scheme constitutes, in our opinion, a good choice for the OPS/OBS node since it can support applications requiring traffic broadcasting or multicasting such as video-on-demand and video/audio conferencing. 2.1.2. Waiting unit (WU) The WU is used for contention resolution occurring in the output ports. It is composed of a set of shared multiwavelengths FDL buffers. Two FDL lengths are used: the packet time slot duration (say, TS) for packets, and a duration equal to SeglxTS for segments, where Segl is the number of packets in a segment. The first length corresponds to the delay required for one packet and the second one corresponds to the delay required for a segment composed of Segl packets. Feed-backward FDL buffers [8,13], which may increase the buffering capacity of the node, are used. They allow the possibility that a packet/segment emerging from an FDL to be buffered more than once into the FDL. This situation may arise if successive contentions occur. The WU also contains a set of full range wavelength converters used for FDL buffer conflicts resolution [6]. 2.1.3. Input processing unit (IPU) An IPU is associated with each input channel. It is composed of the following objects: • a synchronization module that is used to synchronize the arriving traffic units (optical packet, data burst, and burst header packet) and align them with switching time slots boundaries. More details about an OPS/OBS node synchronization are presented in the following subsection; • an optical component, which is based on the optical label swapping (OLS) technology [8], is used to extract the optical header of an incoming packet without payload optical/electrical/optical conversion; • an Electrical/Optical converter that is used for optical packet/burst header conversion for electronic processing; • an FDL buffer that is used for packet payload buffering during the packet header processing; and • Two optical gates: an optical packet gate (OPG), and an optical burst gate (OBG) that are used to treat the packet and the burst at the node entrance.

2.1.4. Output processing unit (OPU) An OPU is associated with each output channel. It has the following components: • A full range wavelength converter that is used for output port contention resolution

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• An Electrical/Optical converter that is used to convert a packet or a burst header in the optical domain after being treated by the SCU • An OLS component linking a packet header with its associated packet payload. • Two optical gates (OPG, OBG) making the transmission of packets and bursts on the same output channel possible.

2.1.5. Switch control unit (SCU) The SCU is used to supervise the SFU functioning. It handles information related to the availability of each wavelength on every output port and the availability of buffering units. This is useful for the reservation of the needed resources (e.g., wavelengths, FDL buffers), as well as for contention resolution needs. The SCU creates and maintains a forwarding table and is responsible for configuring the SFU. It manages signaling packets between OPS/ OBS nodes to optimize burst or packet transmission, reserves the suitable output channel and FDL buffers, configures the appropriate input and output processing units and updates the forwarding table in order to switch the arriving unit on pre-established virtual optical circuit. The SCU supervises input/output processing units and controls the state of optical gates based on signaling information. It opens the OBG or the OPG gate depending on the incoming unit type. Today, the lack of fast, scalable, and robust optical bitlevel processing technologies means that the SCU can only be implemented electronically. 2.2. OPS/OBS node synchronization 2.2.1. Synchronous vs. asynchronous OPS networks Optical packet-switched networks can be classified into two categories: synchronous (slotted) and asynchronous (unslotted) networks. In a synchronous network [6,8], time is slotted, and the switch fabric at each individual node can only be reconfigured at the beginning of a time slot. All packets in a synchronous network have the same size, and the duration of a time slot is equal to the sum of the packet size and the optical header length (plus appropriate guard bands). Due to variable link propagation delays, packets arriving at a node over different interfaces may not be aligned with the local clock. Therefore, synchronization stages are necessary to synchronize arriving packets and align them with switching time slots boundaries. A typical synchronization stage that consists of a series of switches and delay lines is presented in [6,9]. In an asynchronous network [6,8], the packets may or may not have the same size, and the packets arrive and enter the switch without being aligned. Therefore, the packet-by-packet switch action could take place at any point in time. This can leads to contention of different incoming packets for the same outgoing resource.

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Obviously, in unslotted networks, the chance for contention is larger because the behavior of the packets is more unpredictable and less regulated [7]. Therefore, more buffering capacity is needed to provide reasonable performance using an unslotted transmission scheme. Having more delay lines means increasing the port count of the switch fabric and can be a major concern in the network cost computation. 2.2.2. Synchronous vs. asynchronous OBS networks Similar to optical packet-switched networks OBS networks, can be divided into slotted and unslotted categories [7]. In slotted OBS networks, control and data channels are divided into fixed-size time slots. Each control slot is further divided into several BHP (Burst Header Packet) slots with fixed duration. The data burst can be as long as a single or a multiple number of data slots. Therefore, in a slotted transmission mechanism, the offset time as well as the duration of the data burst and its BHP, will be expressed in terms of slots [7]. Furthermore, the OBS core node must align all incoming optical data bursts to the slot boundaries prior to allowing them to enter the switch fabric. In an unslotted OBS network [7], data bursts and their BHPs can be transmitted at any time and do not have to be delayed until the next time slot boundary. However, in such networks, the start and the end of a data burst must still be specified using some predefined time units. These units of time have a much finer granularity compared to data time slots and are typically on the order of clock cycle. Like in an OPS network, an unslotted optical burst switching technique may lead to higher burst loss probability due to unpredictable burst arrival characteristics [7]. 2.2.3. Synchronous OPS/OBS node As it is presented above, a synchronous optical transmission technique performs much better than an asynchronous technique [6–8]. For that reason, we have opted for a slotted optical packet and burst switching technique during the design of the proposed OPS/OBS node architecture. In a synchronous OPS/OBS network, control and data channels are divided into fixed-size time slots. All optical packets have the same size. Each packet is placed inside a time slot, which has a longer duration than the packet to provide guard time. A data burst length is equal to some multiple time slot durations. The offset time, as well as the duration of a burst header packet (BHP), is expressed in terms of time slots. Synchronization stages are used to align all incoming optical packets/bursts with switching time slots boundaries. 2.3. OPS/OBS switching The proposed OPS/OBS node architecture performs packet and burst switching depending on the received data unit type.

2.3.1. Packets switching Arriving packets are de-multiplexed into individual wavelengths, if needed. Each packet is then treated by the corresponding input processing unit. First, it passes through the synchronization stage to be aligned to its time slot boundary. Then, its header is optically extracted by the OLS component. While the header is converted to electrical form and so forwarded to the switch control unit for processing, the corresponding packet payload is inserted in the FDL buffer. The SCU processes the header information and determines the appropriate output port and wavelength from the packet routing information (such as VOC Identifier). In the case of output channel availability, the SCU configures the SFU to carry the packet payload to the corresponding OPU. At the same time, the packet header is sent to the same OPU, where it is converted into an optical form. Finally, the packet header and payload are transmitted to the next node. The output channel unavailability leads to a contention problem which is resolved by the SCU according to the contention resolution scheme that will be detailed in a following section. 2.3.2. Burst switching The burst transmission is preceded by a control packet that is used to establish a virtual optical circuit (VOC). The latter is a concept that is managed in an ATM-like style using circuit identifiers and path identifiers. However, we consider here that the management of VOC is dependent on the priority of the data unit. While higher priorities see their connections guaranteed during the transmission, lower priority units may see their VOC identifiers modified during their travel in order to resolve contention. At each intermediate OPS/OBS node, SCU configures the appropriate IPU to receive the arriving unit. It mainly closes the OPG and opens the OBG. If the intended output channel is available when the burst arrives, SCU configures the associated OPU (closes the OBG and opens the OPG), and instructs SFU to let the data burst pass through. Like the packet switching, the output channel unavailability attempts resolving the contention of segments by the SCU. 3. OPS/OBS signaling protocols As seen above, the main characteristic of our OPS/OBS node is its ability to handle two traffic types: packet-based and burst-based traffic types. For each traffic type, an appropriate signaling protocol is needed from the ingress nodes and between the OPS/OBS nodes. 3.1. Packet-based traffic signaling protocol This protocol is inspired by one used by ATM considering the efficiency of this technology in terms of network resources utilization and QoS support [15]. It requires that the transmission of a packet is preceded by the set up of a virtual optical communication circuit [15]. Such VOC defines a route between the source and the destination

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composed by an association of fiber links and wavelengths along the chosen route and passing through FDLs. Similar to an ATM cell [15], a packet is assumed to have a fixed-length payload and optical header. The signaling protocol mainly considers the following control information: • Routing information: an optical packet is switched based on the VOPI (Virtual Optical Path Identifier) and the VOCI (Virtual Optical Circuit Identifier) values found in the packet header. A VOPI is the identifier of the input optical channel, which is composed of an input port identifier (IPI) and an input wavelength identifier (IWI). VOCI is the identifier of the optical virtual circuit allocated in the input optical channel. • Traffic priority: This specifies the packet priority. It is used during the signaling step for the needed resources (e.g., wavelength, and FDL buffer) reservation, as well as in case of contention resolution. • Complementary Information: This specifies several types of information that are useful such as the type of packet (normal/deviated packet) and conformance to the traffic contract. Lost/erroneous optical packets are assumed to be reinserted in the traffic based on end-user application timeout, error control, or emulated protocols. 3.2. Burst-based traffic signaling protocol With regards to the performance of the burst assembly mechanism and the JET-like signaling protocol proposed in [10], we keep the same burst structure and signaling technique for bursty traffic handling over an OPS/OBS network. However, some signaling features need to be added to cope with contention decisions. An optical data burst is a pure payload, which is made of a set of fixed-length segments assembled in a decreasing order of priority. A segment is composed of a set of packets having the same priority level. Using the JET-like signaling protocol, each burst is preceded by a control packet (BHP: Burst Header Packet) carrying control information related to a burst, e.g. offset time and routing information, as well as control information associated with each segment of the burst including segment priority and segment length. The following control information is considered for a burst specification: • Offset time: It specifies the period of time separating the control packet and the associated burst. It is used during the signaling phase for resource reservation. In a synchronous OPS/OBS network, the offset time is expressed in terms of time slots. • Routing information: It indicates the destination of the burst and used during the setup up of the VOC that is needed for the burst transmission.

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• Burst composition: It is specified by the number of segments of each traffic priority in the burst. Combined with the first control information (offset time), this information allows each intermediate node to know the priority and the arrival time of each segment of the burst, which is necessary for resource reservation and contention resolution. Several issues and challenges arise when implementing burst segmentation. These may lead to unnecessary losses: • Forward information of dropping: When a segment inside a burst is dropped, the related header, which is forwarded before overlapping occurs, will still contain the original information about the entire burst. If downstream nodes are unaware of such truncation, then it is possible that the truncated bursts are subject to new contention, even though the contending segments have been previously dropped. • Segment boundary detection: Segment boundaries are transparent to intermediate nodes that switch the segmented burst. Synchronization to detect segment starting point may, however, lead to uncontrolled errors if segments are not separated. A simple resolution of this problem is explained below assuming that bursts are segmented using equal size segments, which contain a fixed number of packets. Segments are organized within a burst following an increasing order of their priorities. 4. QoS-based contention resolution A contention problem occurs when the resource to which the data unit is directed is not available. The contention resolution scheme that we propose in this paper combines optical buffering and wavelength conversion techniques. It is performed by the SCU and uses WU and OPU converters. It is based on a differentiated QoS provision. 4.1. Contention resolution characteristics 4.1.1. At the ingress node The sender node assigns a wavelength to a generated unit after its segmentation if the unit is a burst. It estimates the time needed to build a path, reserves resources locally, and allocates an offset time to the burst. It then attempts to construct a wavelength path based on information collected from its neighbors about the availability of wavelengths and the use of their resources to the right destination. The ingress node does not observe contention. However, it contributes in offering better QoS to high-level priority bursts and reducing segment losses. This is done by observing a good approach to estimate the offset times and the neighbor selection to which it forwards the control packets (for high-level priority bursts).

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4.1.2. At an OPS/OBS node The contention resolution mechanism can be presented as follows. When two traffic units contend for the same output port and wavelength, the lower priority unit is routed to another available wavelength. If no wavelength is available, a FDL buffer is used. Depending on the contending unit types, three cases are possible: • The contention occurs between two packets: The higher priority packet is directed to its original output port, while the lower priority packet is stored in one of the available packet FDL buffers. This packet may be converted into another wavelength if its original wavelength is not available. If no FDL is available, the packet is dropped. • The contention occurs between two bursts: In this case, the SCU compares the priorities of conflicting segments. The higher priority segment is switched to the appropriate output port, whereas the other segment is stored in one of the segment FDL buffers. The lower priority segment may be converted into another wavelength if it is necessary. If no segment FDL buffer is available, the segment is dropped. • The contention occurs between a packet and a burst: This means that the packet is in conflict with one of the burst segments. In the case where the two units have not the same priority, the higher priority unit is directed to the intended output port and the other is switched to an appropriate FDL buffer. If no FDL buffer is available, the lower priority unit is dropped. In the case where the two units have the same priority, the segment is directed to its original output port, while the packet is switched to an appropriate FDL if available or dropped. Using feed-backward FDL, a traffic unit (packet, segment) emerging from the WU re-enters the switch. Thus a contention may occur between a new arriving traffic unit and a delayed traffic unit, or between two delayed traffic units. In these cases, the choice of the traffic unit to delay is done based on the conflicting units priority levels. If the contending units are of the same priority, the choice is done based on the WU-visits numbers, and the traffic unit with the smallest WU-visits number is favored. If contention occurs between a packet and a segment, the segment is favored regardless of the packet WU-visits number. 4.1.3. At the egress node Segment order is fixed at the egress nodes after receiving all segments. Dropped segment are assumed to be reinserted in the traffic based on end-user application timeout, error control, or emulated protocols. Finally, egress nodes are assumed to contribute to the segment loss reduction by sending the appropriate information to the burst originator in order to help adapting offset time allocation.

4.2. Wavelength conversion/ Buffering processing In the case where the contention resolution is made using the wavelength conversion technique, the SCU creates a control packet and sends it to all remainder VOC in order to update information related to packet/burst switching in all forwarding tables. If the contention resolution is made by the optical buffering technique, the SCU chooses an appropriate FDL buffer in the WU, and configures the SFU to transmit the lower priority data unit (packet payload, segment) to the selected FDL buffer. During a packet payload storage, the packet header is buffered in the SCU using electronic buffers (RAM). According to the feed-backward buffers utilization, a data unit traverses the FDL, and re-enters the switch. If several contentions occur, a traffic unit may be buffered more several times. To prevent an infinite FDL looping, a threshold corresponding to a maximal FDL delay is imposed. If it is exceeded, the contending data unit is dropped. When a segment inside a burst is delayed or dropped, the SCU creates a control packet and sends it to all remainder VOC in order to update information related to the associated burst composition. Otherwise, downstream nodes activities will be based on false information, which may lead to bogus decision, particularly with contention. In fact, it is possible that the truncated bursts are subject to new contention, even though the contending segments have been previously dropped or delayed. When it is accepted, a delayed traffic unit (packet, segment) is transmitted to its egress node through the original established VOC. The transmission of a delayed segment is preceded by a control packet created by the SCU, and sent to all remainder VOCs for needed resources reservations. 5. Analytical model In this section, we present the analytical model developed for the performance evaluation of the proposed node architecture. 5.1. OPS/OBS node characteristics assumptions We consider a system with N traffic classes labeled 0, 1, . . ., N1, in a decreasing priority order. The traffic of each class is composed of two varieties of fixed-length traffic units; packets and segments. A segment is composed of a fixed number of optical packets of the same traffic class. Let T, Segl and STR denote a packet length, a segment length and the segments-traffic ratio, respectively. Let m and n denote a packet and a segment maximal WU-visits number, respectively. Let PCi,j, 0 6 j 6 m, represents the traffic sub-class consisting of packets of class i which have been switched j times to the WU, and let SCi,j, 0 6 j 6 n, be the segments of class i, that have visited WU for j times. PCi,0 and SCi,0 represent the new arriving packets and segments of class i.

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Moreover, we assume that arriving packets and segments of class i that are addressed to a specific output port of a node follow the Poisson process with rate ki and rate cI, respectively. Let k be the number of wavelengths available at each output port, and let us assume that each OPS/ OBS node is equipped with a WU with a large buffering capability, insuring a permanent availability of the needed storage capacity required by any contention resolution. Optical units addressed to a given output port are transmitted with their priorities and integrate the adequate traffic subclasses. Finally, we denote by pi,j the blocking probability of a packet of the PCi,j traffic sub-class, and qi,j the blocking probabilities of a segment of the traffic sub-class SCi,j. 5.2. OPS/OBS node modeling Once the above assumptions are made, it becomes easy to model an output port at an OPS/OBS node. This model, which is depicted by Fig. 2, is an open queuing network system composed of two stations. Station 1, which represents the output port transmission unit has a M/D/k/k preemptive priority type. Station 2, which represents the waiting unit, has an M/D/1 queue type. The whole system is assumed to handle N.[(m + 1) + (n + 1)] customers classes corresponding to the N.(m + 1) packet sub-classes and the N.(n + 1) segment sub-classes. Let us consider the path followed by a customer (i.e., packet, segment) through the queuing network. Assume that the arriving customer is a packet of class i, i.e. an element of sub-class PCi,0. This customer can be serviced

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immediately or be blocked. In the first case, a transmission server at station 1 is allocated to this customer during a fixed service time T (equals to the packet length). Then the customer leaves the system. In the second case, the customer is sent to station 2 where it can be served during a deterministic service time T (packet length). Once its service at station 2 is completed, it moves to node 1 as a customer of the traffic sub-class PCi,1. It tries again to get a transmission server at station 1; and so on, until it succeeds to get hold of a transmission server at station 1 or it is dropped. Note that each time the customer returns to station 1, its traffic sub-class is updated according to the previous definition PCi,1 PCi,2,. . .PCi,n.. Because upper bound is fixed in terms of packet and segment WU-visits number, a customer of the traffic sub-classes: PCi,m and SCi,n, which cannot seize one transmission server at the transmission unit, will be dropped. 5.3. Model analysis Two metrics have been chosen to evaluate the OPS/OBS node performance: the packets-loss mean rate (PLMR) and the packet-blocking mean delay (PBMD). In the following subsection, we present the analysis of these performance metrics. 5.3.1. Performance metrics analysis Let PLMRi and PBMDi denote the packet loss mean rate and the packet-blocking mean delay for traffic class i, 0 6 i 6 N. Based on the proposed queuing network model,

Fig. 2. Queuing network model of an output port of an OPS/OBS node.

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we can establish the following expressions for evaluating the considered performance metrics for traffic class i. Qm Qn ð1  STRÞ  j¼0 pi;j þ STR  Segl  j¼0 qi;j ð1Þ PLMRi ¼ ð1  STRÞ þ STR  Segl 2 PBMDi ¼4



ð1  STRÞ: 1 

Qm

j¼0 p i;j

P

m X

j:T :ð1  pi;j Þ:

SUBMDi ¼

n X

j1 Y

j:T :Segl:ð1  qi;j Þ:

The above expressions can be proved as follows. We consider a sample of C traffic units of class i destined to the same output port of an OPS/OBS node. This set of traffic units is composed of C * STR segment-units and (1STR) * C packet-units. Let PLPi and SLPi denote the loss probability of a packet-unit and a segment-unit of class i. Based on the aforementioned analytical model, PLPi and SLPi can be expressed as follows: m n Y Y pi;j SLP i ¼ qi;j ð3Þ PLP i ¼ j¼0

j1 Y

ð9Þ

qi;k

k¼0

j¼1

ð2Þ

ð8Þ

pi;k

k¼0

j¼1

Qj1 m j¼1 j:T :ð1  p i;j Þ: k¼0 p i;k

ðð1  STRÞ þ STR:SeglÞ:ð1  PLMRi Þ  P Q Qj1 3 n STR:Segl: 1  nj¼0 qi;j j¼1 j:T :Segl:ð1  qi;j Þ: k¼0 qi;k 5 þ ðð1  STRÞ þ STR:SeglÞ:ð1  PLMRi Þ

j¼0

PUBMDi ¼

Expression 8 can be explained as follows. An optical packet can be delayed j times, where 0 6 j 6 m, and the probability that a packet is delayed Qj1j times (i.e., during a period of time j.T), is equal to k¼0 pi;k . Expression 9 can be explained in a similar manner. Let SPBDi be the sum over all accepted packets among all packets transported by the considered flow of the packet blocking delay. SPBDi is given by the following expression: SPBDi ¼ C  ð1  STRÞ  PUBMDi þ Segl  C  STR ð10Þ

 SUBMDi

By substituting PUBMDi and SUBMDi by their expressions in (8), we can rewrite the expression of (9) as follows: " j1 m X Y SPBDi ¼ C  ð1  STRÞ  j:T :ð1  pi;j Þ: pi;k k¼0

j¼1

#

These expressions can be explained as follows. A traffic unit (packet or segment) is dropped if it exceeds the FDL delay threshold (i.e., the maximal WU-visits number). We notice that these expressions are insensible to the traffic model. Here, we assume that the traffic model follows the Poisson process. Let TPNi be the total number of packets transported by the considered flow of class i. We have:

Let TAPNi denotes the total number of accepted packets among all packets transported by the considered flow of class i. TAPNi is given by the following expression:

TPN i ¼ ð1  STRÞ  C þ Segl  C  STR

TAPN i ¼ TPN i  ð1  PLMRi Þ

ð4Þ

Let TLPNi be the total number of lost packets among the total arrived packets of class i. TLPNi is given by the following expression: TLPN i ¼ C  ð1  STRÞ  PLP i þ C  STR  Segl  SLP i

ð5Þ

By substituting PLPi and SLPi by their expressions in (3), we can rewrite expression (5) as follows: m Y pi;j þ C  STR  Segl TLPN i ¼ C  ð1  STRÞ  j¼0



n Y

qi;j

ð6Þ

j¼0

By definition, we have: PLMRi ¼

TLPN i TPN i

ð7Þ

By substituting TPNi and PLPNi by their expressions in (4) and (6), we can obtain the expression of the PLMRi as it is presented in (1). Let now PUBMDi and SUBMDi denote the blocking mean delay of an accepted packet-unit and an accepted segment-unit of the traffic class i. These are given by the following expressions:

þSegl  C  STR 

n X

j:T :Segl:ð1  qi;j Þ:

j¼1

j1 Y

qi;k

k¼0

ð11Þ

ð12Þ

Substituting TPNi by its expression in (4) gives us: TAPN i ¼ ðð1  STRÞ  C þ Segl  C  STRÞ  ð1  PLMRi Þ

ð13Þ

By definition, we also have: PBMDi ¼

SPBDi TAPN i

ð14Þ

By substituting SPBDi and TAPNi by their expressions in (10) and (12), we can obtain the expression of the PBMDi as it is presented in expression (2). As it is shown in the established expressions of the considered performance metrics, we notice that the evaluation of these performance metrics require the analysis of the blocking probabilities for the considered traffic sub-classes (pi,j, 0 6 j 6 m, qi,j, 0 6 j 6 n). This analysis has been conducted based on the use of a new conservation law [12], which was initially proposed for the evaluation of burst blocking probabilities in an OBS network with multiple priority classes, unequal mean burst lengths, and in the presence of pre-emption scheme. A brief presentation of such new conservation law is presented in Appendix A.

A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

5.3.2. Blocking probabilities analysis In order to analyze the blocking probabilities of the different traffic sub-classes of our analytical model, we follow the analysis based on the new conservation law (see Appendix A). We recall that we consider N * (m + 1) + N * (n + 1) traffic sub-classes labeled and ordered in a decreasing order of priority as follows:

1007

Based on the above presented new conservation law, we could establish the following expression for the analysis of q0,j, the blocking probability of the traffic sub-class SC0,j, 1 6 j 6 n: ! j X s s s q0;j ¼ B0;j þ F 0;j ; where B0;j ¼ E u0;i ; k ; i¼0

Pj1

  i¼0 c0;i Bs0;j  Bs0;j1 c0;j

SC0;0 ;. ..; SC0;j ; ... :;SC0;n ;PC0;0 ;.. .;PC0;j ; ... ;PC0;m ; ... ... ... ... ... ... ... ... ... .. ... ... ... ... ... ... ... ... . ;

F s0;j ¼

SCi;0 ; ... ;SCk;j ; ... :;SCk;n ;PCk;0 ; .. .;PCk;j ;.. .;PCk;m ;

Similarly, we can establish the expression of p0,0, the blocking probability of the traffic sub-class PC0,0, which represents the highest priority packets sub-class.

... ... ... ... ... ... ... ... ... .. ... ... ... ... ... ... ... ... . ; SCN 1;0 ; ... ;SCN 1;j ;.. .:; SCN 1;n ; PCN 1;0 ;. ..; PCN 1;j ;.. .;PCN 1;m ;

p0;0 ¼ BP0;0 þ F P0;0 Let ki,j and qi,j denote the arrival rate and the traffic intensity of the traffic sub-classes PCi,j, 0 6 i 6 N  1, 0 6 j 6 m. The parameters ki,j and qi,j are given by the following expressions: ki;j ¼ ki;0 :

j1 Y

pi;k for 1 6 j 6 m;

¼

k0;0 þ

n X

k¼0 c0;k

¼ !

k0;0

 ðBP0;0  BS0;n Þ; where ð21Þ

c0;k

ki;0 ¼ ki

"

ð15Þ

 Segl:T :

qi;j ¼ T :ki;j ¼ qi;0 :

j1 Y

n X k¼0

pi;k for 1 6 j 6 m;

k¼0

qi;0 ¼ T :ki;0 ¼ T :ki

ð16Þ

Let ci,j and ui,j denote the arrival rate and the traffic intensity of the traffic sub-classes SCi,j, 0 6 i 6 N  1, 0 6 j 6 n. ci,j and ui,j are given by the following expressions: j1 Y

aP0;0

¼

Pn

EðaP0;0 ; kÞ; F P0;0

k¼0

k¼0

ci;j ¼ ci;0 :

BP0;0

ð20Þ

qi;k for j P 1;

ci;0 ¼ ci

ð17Þ

k¼0

ui;j ¼ Segl:T :ci;j ¼ ui;0 :

j1 Y

qi;k for j P 1;

k¼0

ui;0 ¼ Segl:T :ci;0

ð18Þ

Let BPi,j and FPi,j, 0 6 i 6 N  1, 0 6 j 6 m, denote the blocking probability due to lack of transmission servers (wavelengths) and the preemption probability of the traffic sub-class PCi,j by higher priorities traffic sub-classes. Let BSi;j and F Si;j , 0 6 i 6 N  1, 0 6 j 6 n, denote the blocking probability due to lack of wavelengths and the preemption probability of the traffic sub-class SCi,j by the traffic subclasses of higher priorities. Given that a preemptive priority service discipline is assumed for traffic units transmission, and SC0,0, is supposed to be the highest priority traffic sub-class, the blocking probability of the traffic sub-class SC0,0, q0,0, is given by the following expression: uk0;0 =k! q0;0 ¼ Eðu0;0 ; kÞ ¼ Pi¼k i i¼0 u0;0 =i!

ð19Þ

k0;0 :ð1 

c0;k :ð1  BS0;k Þ P P B0;0 Þ þ nj¼0 c0;j :ð1

k0;0 :ð1  BP0;0 Þ P þT : k0;0 :ð1  BP0;0 Þ þ nj¼0 c0;j :ð1  BS0;j Þ

 BS0;j Þ

#

Following the same way, we can analyze the blocking probability of the traffic sub-class PC0,j, 1 6 j 6 m. The expression of p0,j is given by: p0;j ¼ Bp0;j þ F p0;j ; where Bp0;j ¼ Eðap0;j ;kÞ; P Pj1  n c0;k þ k¼0 k0;k k¼0 F p0;j ¼ :ðBp0;j  Bp0;j1 Þ k0;j ! j n X X p a0;j ¼ c0;k þ k0;k k¼0

"

k¼0 n X

c0;k :ð1  Bs0;k Þ Pj p s k¼0 l¼0 c0;l :ð1  B0;l Þ þ i¼0 k0;i :ð1  B0;i Þ # j X k0;k :ð1  Bp0;k Þ þT ð22Þ Pn Pj p s k¼0 l¼0 c0;l :ð1  B0;l Þ þ i¼0 k0;i :ð1  B0;i Þ

 Segl:T :

Pn

In the above, we have presented the expressions established for the analysis of the blocking probabilities of the different traffic sub-classes of the traffic class 0. Following the same way, we can analyze the blocking probabilities of the different traffic sub-classes of each traffic class i, 1 6 i 6 N  1. Let qi,j, 0 6 j 6 n denotes the blocking probability of the traffic sub-class SCi,j. For 1 6 j, qi,j is given by the following expression:

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A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

Qi;j ¼ BSi;j þ F Si;j ; where

pi,0 is given by the next expression:

BSi;j

pi;0 ¼ BPi;0 þ F Pi;0 ; where P Pm Pi Pn ð i1 l¼0 k¼0 kl;k þ l¼0 k¼0 cl;k Þ BPi;0 ¼ EðaPi;0 ; kÞ; F Pi;0 ¼ ki;0

¼ EðaSi;j kÞ; ð

F Si;j ¼

Pi1 Pn

þ

k¼0 cl;k

l¼0

Pi1 Pm

k¼0 kl;k

l¼0

þ

Pj1

k¼0 ci;k Þ

ci;j

 ðBPi;0  BSi;n Þ " # i1 X m i X n X X P kl;k þ cl;k þ ki;0 ai;0 ¼

 ðBSi;j  BSi;j1 Þ " # j i1 X n i1 X m X X X S ai;j ¼ cl;k þ kl;k þ ci;k l¼0 k¼0

P

i1 l¼0

l¼0 k¼0

n P

cl;k 1  BSl;k

þ

l¼0 k¼0

k¼0

T Pi1 Pm

P k¼0 ki;k ð1  Bl;k Þ þ

l¼0

Pj

S k¼0 ð1  Bi;k Þ

k¼0

"

"

i1 X X n

c :ð1  BSj;k Þ þ k¼0 l;k

 Segl:

#

Xj

 Pi1 Pm l¼0

"  Segl:

c ð1  BSi;k Þ k¼0 i;k

i1 X n X

P k¼0 kl;k ð1  Bl;k Þ þ

i X n X

T Pi Pn l¼0

S P k¼0 cl;k ð1  Bl;k Þ þ ki;0 ð1  Bi;0 Þ

cl;k ð1  BSl;k Þ

l¼0 k¼0

i¼0

þ

l¼0 k¼0

#

þ

kl;k ð1  BPl;k Þ

ð23Þ

" i1 X m X

## kl;k ð1  BPl;k Þ þ ki;0 ð1  BPi;0 Þ

ð26Þ

l¼0 k¼0

i¼0 k¼0

qi,0 is given by this expression: qi;0 ¼ BSi;0 þ F Si;0 ;

where P

BSi;0 ¼ EðaSi;0 ; kÞ;F Si;0 ¼

6. Numerical results

i1 Pn l¼0 k¼0 cl;k

Pi1 Pm

þ

k¼0 kl;k

l¼0

In order to evaluate the performance of the OPS/BS node architecture and validate our analytical model, a simulation model has been developed. In the sequel we will present the implemented simulation model and discuss some of the most important numerical results.



ci;0

 ðBSi;0  BPi1;m Þ " # i1 X n i1 X m X X S ai;0 ¼ cl;k þ kl;k þ ci;0 l¼0 k¼0

6.1. Simulation model

l¼0 k¼0

T

P

Pi1 Pm i1 Pn S l¼0 k¼0 cl;k ð1  Bl;k Þ þ l¼0 k¼0 kl;k

"

"

 Segl:

i1 X n X



1  BPl;k



þ ci;0 ð1  BSi;0 Þ

# cl;k :ð1  BSl;k Þ þ ci;0 ð1  BSi;0 Þ

l¼0 k¼0

þ

i1 X

m X

# kl;k ð1  BPl;k Þ

ð24Þ

l¼0 k¼0

Let pi,j, 0 6 j 6 m denotes the blocking probability of the traffic sub-class PCi,j. For 1 6 j, pi,j is given by the following expression: pi;j ¼ BPi;j þ F Pi;j ; where P BPi;j

¼ EðaPi;j ;kÞ; F Pi;j

¼

i1 Pm l¼0 k¼0 kl;k

þ

Pi Pn

k¼0 cl;k

l¼0

þ

Pj1

k¼0 ki;k



ki;j

 ðBPi;j  BPi;j1 Þ " aPi;j

¼

i1 X m X

kl;k þ

i X n X

l¼0 k¼0

cl;k þ

l¼0 k¼0

 Pi1 Pm l¼0

"  Segl:

j X

#

Pi

l¼0

T Pn

S k¼0 cl;k ð1  Bl;k Þ þ

Pj

P k¼0 ki;k ð1  Bi;k Þ

cl;k ð1  BSl;k Þ

l¼0 k¼0

" i1 X m X

þ

l¼0 k¼0

kl;k ð1  BPl;k Þ þ

j X k¼0

6.1.2. Traffic model The traffic generated by an input channel is composed of two kinds of traffic units; packets and bursts. The type of a new traffic unit is arbitrary generated based on a bursty traffic ratio (BTR) system parameter. The inter arrival time between two successive units received on the same input channel is assumed to be exponentially distributed with a mean value called MTSSU (mean time separating two successive units). The traffic generated by an input channel is assumed to be uniformly distributed between the two considered output channels.

ki;k

k¼0

P k¼0 kl;k ð1  Bl;k Þ þ

i X n X

6.1.1. Node configuration The configuration of the simulated node supposes two input and output optical channels with a transmission capacity equal to 2.5 Gbit/s. The node is equipped with a WU having a large buffering capacity insuring the availability of the needed storage capacity for any contention resolution.

## ki;k ð1  BPi;k Þ

ð25Þ

6.1.3. Packets priorities We have found it interesting to consider more than two priorities for the arriving packets. Several priorities allow, in fact, the definition of various node behaviors for different traffic requirements. In our case, we have considered four packets priorities, denoted by 0, 1, 2 and 3. Priority 0 is the highest one; it has the lowest traffic loss and transmission delay tolerance. Priority 3 is the lowest one. We assume that the input traffic ratios of individual packet

A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

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priorities are 10%, 20%, 30%, and 40% for priority levels 0, 1, 2, and 3, respectively. It is also assumed that all packets have the same length of (1250 bytes). 6.1.4. Burst composition and generation A burst is composed of an arbitrary number of segments. A segment is composed of a fixed number (Segl: Segment length) of packets with the same traffic priority. The burst length (Burstl) is assumed to be a random variable that is uniformly generated in the interval [Min_burstl, Max_Burstl], where Min_Burstl and Max_Burstl are two input system parameters representing the minimum and the maximum burst length, respectively. 6.1.5. Performance metrics Two metrics have been chosen to evaluate the performances of our OPS/OBS node architecture: the packetsloss mean rate and the average packet-blocking delay. The following input parameters have been considered during the performance evaluation: the packet length (T), segment length (Segl), mean time separating two successive units (MTSSU), packet maximum WU-visits number (m), segment maximum WU-visits number (n), and bursty traffic ratio (BTR). 6.1.6. Simulation model accuracy We have found it interesting to present a clear indication about the accuracy of the developed simulation model before presenting the simulation results. The validity of the simulation model is ensured by the use of random generators based on the well known generator of pseudo-random uniformly distributed numbers RAND. Predefined in the programming language C libraries, this generator belongs to a class of multiplicative linear congruential pseudo-random numbers generators (LC-PRNGs), which are well proved [16,17]. In addition to the use of suitable random generators for the generation of the input traffic units, simulations experiments are conducted using appropriate sample-size, calculated using a well used statistical method, which may improve the credibility of the developed simulation model.

Fig. 3. packets-loss mean rate versus the mean time separating two successive units.

the developed analytical model match with the simulation results, which affirms the validity of the developed analytical model. The figure shows that the packets-loss mean rate decreases with the increase of MTSSU. This corresponds to the traffic charge decrease, and so to the decrease of the probability of contention. The figure illustrates that, a service differentiation is guaranteed and a high performance (i.e. low packets-loss) is ensured for high-priority traffic classes (i.e., classes 0, and 1). Fig. 4 presents the analytical and simulation results for the impact of Segl on the packets-loss mean rate, when BTR = 100%, T = 5 ls, MTTSSU = 10 * T, n = 2 visits, and Burstl = 5 segments. Similar to Fig. 3, this figure

6.2. Numerical results In this subsection, we present the numerical results we have obtained to show how the input parameters affect the performance of the proposed OPS/OBS node architecture. We also compare the analysis results with the results obtained from simulation in order to show the validity of the analytic model. 6.2.1. Traffic loss Fig. 3 shows the analysis and simulation results for the impact of MTSSU on the packets-loss mean rate, where we fix BTR = 100%, T = 5 ls, Segl = 10 packets, n = 2 visits, Burstl = 5 segments. We observe that, for all traffic priorities, the packet loss probability obtained through

Fig. 4. Packets-loss mean rate vs segment length.

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A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

asserts that the analytic results are very close to the results obtained from simulation analysis. Fig. 4 shows that a very weak traffic loss is experienced for the high-priority traffic (0, 1), and an acceptable performance is offered to the low-priorities traffic, say priorities (2, 3). We observe that, the packets-loss mean rate increases with the increase of number Segl. This can be explained by noting that the drop of a segment, due to a contention resolution, leads certainly to the drop of Segl packets. Therefore, the increase of Segl is accompanied by the increase of the number of dropped packets, and also the increase the packet-loss mean rate. Fig. 5 presents the analytic and simulation results for the impact of the packet FDL delay threshold on the packetsloss mean rate, when BTR = 0%, T = 5 ls, and MTTSSU = 0.5 * T. We notice that, for all traffic priorities, the packets-loss mean rate obtained through simulation matches with the analytical results. Fig. 5 confirms also that a service differentiation is assured and a high performance is ensured for the high-priority traffic classes (0, 1). We observe that, the increase of the packet FDL delay threshold, decreases the packets-loss mean rate. This can be explained as follows. The increase of the packet FDL delay threshold increases the packet maximum WU-visit number, which reduces the packets-loss mean rate. 6.2.2. Blocking delay Fig. 6 shows the analytic and simulation results for the effect of MTSSU on the packet-blocking mean delay, when BTR = 0%, T = 5 ls, and m = 20 visits. This figure confirms that for all traffic priorities, the average packet-blocking delay obtained throughout the analytical model match with the simulation results. We observe that a service differentiation is guaranteed in terms of transmission delay and high performance (low packet-blocking delay) is ensured for the high-priority traffic priority (0). Also, a tolerable performance is provided for the low-priority traffic classes (2, 3). Fig. 6 also shows that the packet-blocking mean

Fig. 5. Packets-loss mean rate versus a packet FDL delay threshold.

Fig. 6. Average packet-blocking delay versus the mean time separating two successive units.

delay decreases with the increase of the duration of the period separating two successive units. This is because the increase of the mean time forces the decrease of the traffic load on each input channel, which reduces the contention probability, and therefore, the packet-blocking mean delay is decreased. Fig. 7 presents the simulation and analytical results for the impact of the packet length (T) variation on the packetblocking mean delay, when we fix BTR = 0%, MTSSU = 0.5 · T, and m = 20 visits. This figure shows a good agreement between the analytical and simulation results. We observe also that a service differentiation is ensured and a very low packet-blocking delay is guaranteed

Fig. 7. Average packet-blocking delay versus packet length.

A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

Fig. 8. Average packet-blocking delay vs packet FDL delay threshold.

for the high-priority traffic (0). We notice that, for all traffic priorities, the increase of the time slot duration increases the packet-blocking mean delay. This can be explained as follows. The increase of T increases the length of the FDL buffers used for contention resolution, which increases the packet-blocking mean delay. Fig. 8 shows the analytic and simulation results for the impact of the packet FDL delay threshold on the packetblocking mean delay, when BTR = 0%, T = 5 ls, and MTTSSU = 0.5 * T. The figure states that the analytical results are very close to the results obtained from simulation. We notice that a service differentiation is guaranteed and a low packet-blocking delay is provided for the two high-priority traffic classes (i.e., class 0 and class 1) and acceptable performance is given for the low-priority traffic classes (i.e., 2 and 3). The figure shows that the increase of the packet FDL delay threshold increases the packetblocking mean delay. This is because the increase of the packet FDL delay threshold induces the growth of the packet maximum WU-visit number, which increases the average packets-blocking delay. 6.2.3. Analytical model accuracy The results depicted in Figs. 3–8 show a good agreement between the analysis and simulation results in the case when a single traffic-units type is present (BTR = 100%, BTR = 0%). This validates the accuracy of the developed analytical model in this particular case of traffic composition. In order to validate our model in the general cases (i.e., presence of packets and bursts), a low complex configuration (m = n = 1) has been analyzed, where the two considered traffic-units types are present. Our choice in reducing the complexity of the simulation configuration was due to the limits of the available computing resources. Figs. 9 and 10 present the numerical results obtained for the above mentioned configuration, where we fix at

1011

Fig. 9. Packets-loss mean rate versus the mean time separating two successive units where N = 4, m = n = 1, and BTR = 25%.

Fig. 10. Average packet-blocking delay versus the mean time separating two successive units where N = 4, m = n = 1, and BTR = 25%.

BTR = 25% (meaning the presence of packets and bursts), T = 5.0 ls, Segl = 5, and Burstl = 5. The figures show that the analytic results are close to the results obtained from simulation. This validates the accuracy of the developed analytic model for a general configuration of the OPS/ OBS node architecture. 7. Conclusion In this paper, we have proposed a node architecture suitable for optical packet and burst switching. We also have addressed the contention resolution, signaling, and QoS support issues. An ATM-like signaling protocol has been developed for packet-based traffic handling, and a JET-like protocol has been adopted for bursty traffic signaling.

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A. Lazzez et al. / Computer Communications 30 (2007) 999–1014

Based on wavelength conversion and optical buffering techniques, a specific mechanism has been proposed for contention resolution. QoS support has been provided using prioritized optical buffering. This approach assumes that the choice of the traffic unit to delay, in case of contention, is done based on the priority of the conflicting traffic units and the waiting unit occupancy. To evaluate the performance of the proposed architecture, an analytic theoretic model has been developed. The model integrates a new conservation law that we have used to estimate the burst blocking probabilities in an OBS network. A simulation model also has been developed to study the proposed architecture features, and validate the proposed analytical model. The obtained numerical results show a good agreement between analytical and simulation results, which validates the accuracy of the developed theoretical model. A service differentiation is finally shown and a significant low loss and delay is observed for the high-priority traffic. Appendix A. New conservation Law The new conservation law was proposed to evaluate the burst blocking probabilities in an OBS network with multiple priority classes, unequal mean burst lengths, and in the presence of the pre-emption scheme. It constitutes an extension of the original conservation law [12], which was intended for multiple priority classes with equal mean burst length. It considers a single OBS node of an OBS network with n classes of bursts labeled as 1, 2, . . ., n, in a decreasing order of priority. It assumes that for a given output port of the OBS switch, the burst arrival process of class i is a Poisson process with rate ki, and the burst length of class i (Li) is an exponential random variable of rate li = 1/E (Li), where E (Li) denotes the expected values of Li. The bursts are served in order of priority and for each class in the order of their arrivals. When all the channels at a given output port are busy, a new arriving burst of any class will preempt one of the lowest class, if any, or will be blocked otherwise. Sine the burst lengths are exponentially distributed the results for preemptive resume and preemptive non-resume [12] will be identical. This new conservation law provides an exact model for burst blocking probabilities by taking into account the effects of blocking and preemption on the mean overall service time, and can be presented as follows: Let us first define the following variables: • • • •

k: the number of channels used at each output port. qi = ki/li: the offered load of class i. ai: the overall offered load of classes 1, . . ., i. Bi: the blocking probability of class i due to lack of wavelengths. • Fi: the preemption probability of class i by classes 1, . . ., i  1. • Pi: the blocking probability of class i;

Under the above preemptive service discipline, the probability that a burst of class 1 (i.e., the highest priority class) is blocked is given by the well-known Erlang-B formula. qk1 =k! P 1 ¼ B1 ¼ Eðq1 ; kÞ ¼ Pi¼k i i¼0 q1 =i!

ð27Þ

Using the new conservation law, the probability of a burst of class i, i P 2 is given by the following expression. P i ¼ Bi þ F i

Pi1 j¼1 kj Bi ¼ Eðai ; kÞ; F i ¼ ðBi  Bi1 Þ; where ki ! ! i i X X kk ð1  Bk Þ 1 ai ¼ kj Pi l j¼1 k¼1 j¼1 kj ð1  Bj Þ k

ð28Þ

References [1] Georgios I. Papadimitriou, Chrisoula Papazoglou, Andreas S. Pomportsis, Optical switching: switch fabrics, techniques, and architectures, Journal of Lightwave Technology 21 (2) (2003) 384–406. [2] Steinar Bjornstad et al., Optical burst and packet switching: node and network design, contention resolution and quality of service – results from the study in COST 266, in: Proceedings of Seventh International Conference on Telecommunications (ConTEL 2003), Zagreb, Croatia, June 2003. [3] S. Yao, B. Mukherjee, Advances in photonic packet switching: an overview, IEEE Communications Magazine (2000) 84–94. [4] C. Qiao, M. Yoo, Optical burst switching (OBS) a new paradigm for an optical internet, Journal of High Speed Networks 8 (1999) 69–84. [5] A. Lazzez, Y. Khelifi, S. Guemara El Fatmi, N. Boudriga, M.S. Obaidat, Prioritized optical buffering for QoS support in optical switched Networks, in: Proceedings of the SMC’05 (2005 Spring Simulation Multiconference), Applied Telecommunication Symposium (ATS), San Diego, April 2005. [6] Shun Yao, Biswanath Mukherjee, S.J. Ben Yoo, S. Dixit, A unified study of contention-resolution schemes in optical packet-switched networks, IEEE Journal of Lightwave Technology (2003). [7] Farid Farahmand V.M. Vokkarane, J.P. Jue, Practical priority contention resolution for slotted optical burst switching networks, in: Proceedings, First International Workshop on Optical Burst Switching (WOBS 2003), co-located with SPIE OptiComm 2003, Dallas, TX, October 2003. [8] George N. Rouskas, Lisong Xu, Chapter 1: Optical Packet Switching, to appear in Book Optical WDM Networks: Past Lessons and Path Ahead, Kluwer, Massachusetts, 2004. [9] I. Chlamtac et al., CORD: contention resolution by delay lines, IEEE Journal on Selected Areas in Communications 14 (5) (1996) 1014– 1029. [10] Amor Lazzez, Noureddine Boudriga, Sihem Guemara-Elfatmi, Segments-priorities based contention resolution technique for QoS support in optical burst switched networks, in: Proceedings the 12th IEEE Mediterranean Electronical Conference (MELECON 2004), Dubrovnik, Croatia, vol. II, pp. 527–530, May 2004. [11] Yassine Khlifi, Amor Lazzez, Sihem Guemara-Elfatmi, Noureddine Boudriga, Optical packet and burst switching node architecture: Modeling and performance analysis, in: Proceedings of the Eighth IEEE International Conference On Telecommunications (ConTEL05), Zagreb, Croatia, June 2005. [12] Guoping Zeng, Kejie Lu, Imrich Chlamtac, On the conservation law in optical burst switching networks, in: Proceedings of the International Symposium on Performance Evaluation of Computer and Telecommunication Systems, SPECTS’04, pp. 124–129, July 2004.

A. Lazzez et al. / Computer Communications 30 (2007) 999–1014 [13] Georgios I. Papadimitriou, Chrisoula Papazoglou, Andreas S. Pomportsis, Optical switching: switch fabrics, techniques, and architectures, Journal of Lightwave Technology 21 (2) (2003). [14] K.A. McGreer, Arrayed waveguide gratings for wavelength routing, IEEE Communications Magazine 36 (12) (1998) 62–68. [15] J. Boudec, The asynchronous transfer mode: a tutorial, Computer Networks and ISDN Systems 24 (1992) 279–309. [16] K. Pawlikowski, H.-D.J. Jeong, J.-S.R. Lee, On credibility of simulation studies of telecommunication networks, IEEE Communications Magazine 40 (1) (2002) 132–139. [17] M.S. Obaidat, G.I. Papadimitriou (Eds.), Applied System Simulation: Methodologies and Applications, Kluwer (Springer now), MA, 2003.

Amor Lazzez received the Engineering diploma from the high school of computer sciences, Tunisia, in June 1998 and the Master degree in Telecommunication from the high school of communication, Tunisia, in November 2002. He is working toward the Ph.D. degree in the information and communication’s technologies at the high school of communication, Tunisia, where he is currently a researcher at the Security and Telecommunication Networks (CN&S) Laboratory. His active area of research is in optical networks, focusing on the design and analysis of optical burst switched network architectures and protocols.

Yassine Khlifi received the Engineer Diploma and M.S. degrees from Military Academic and High school of communication (Sup’Com) of Tunisia in 1993 and 2001 respectively. He is working toward the Ph.D. degree in the information and communications technologies at the high school of communication, Tunisia, where he is currently a researcher at the Security and Telecommunication Networks (CN&S) Laboratory. His active area of research is in optical networks, focusing on the design and analysis of optical label/packet switched network architectures, protocols and Quality of Service (QoS).

Sihem Guemara El Fatmi received the Ph.D. degree in Computer Science at the university ‘‘P. &M. Curie, Paris VI.’’, France, June 1983, and the ’Habilitation Universitaire’ in Communication Networks and Security at the high school of communication (Sup’Com), Tunisia, May 2004. Dr. Guemara El Fatmi interests cover a large spectrum of themes including communication networks and information security. The development of e-security architectures, and switching issues for optical networks have been the major research activities performed by Dr El Fatmi during the last three years. Dr. Guemara El Fatmi is very active in supervising the research activity of Master and Ph.D. students at Sup’Com. Her contribution to the development of skills of CN&S engineering is noticeable.

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Noureddine Boudriga Prof. Noureddine Boudriga is an internationally known scientist/academic. He received his Ph.D. in Algebraic topology from University Paris XI (France) and his Ph.D. in Computer science from University of Tunis (Tunisia). He is currently a Professor of Telecommunications at University of Carthage, Tunisia and the Director of the Communication Networks and Security Research Laboratory (CNAS) He is the recipient of the Tunisian Presidential award in Science and Research (2004). He has served as the General Director and founder of the Tunisian National Digital Certification Agency. He was involved in very active research and authored or coauthored many chapters and books. He published over 200 refereed journal and conference papers. Prof. Boudriga is the President of the Tunisia Scientific telecommunications Society.

Mohammad S. Obaidat Mohammad S. Obaidat is an internationally well known academic, researcher, and scientist. He received his Ph.D. and M. S. degrees in Computer Engineering with a minor in Computer Science from The Ohio State University, Columbus, Ohio, USA. Dr. Obaidat is currently a full Professor of Computer Science at Monmouth University, NJ, USA. Among his previous positions are Chair of the Department of Computer Science and Director of the Graduate Program at Monmouth University and a faculty member at the City University of New York. He has received extensive research funding. He has authored or co-authored five books and over three hundred (320) refereed scholarly journal and conference articles. Dr. Obaidat has served as a consultant for several corporations and organizations worldwide and is editor of many scholarly journals including being the Chief Editor of the International Journal of Communication Systems published by John Wiley. In 2002, he was the scientific advisor for the World Bank/UN Workshop on Fostering Digital Inclusion. Recently, Dr. Obaidat was awarded the distinguished Nokia Research Fellowship and the Distinguished Fulbright Award. Dr. Obaidat has made pioneering and lasting contributions to the multifacet fields of computer science and engineering. He has guest edited numerous special issues of scholarly journals such as IEEE Transactions on Systems, Man and Cybernetics, Elsevier Performance Evaluation, SIMULATION: Transactions of SCS, Elsevier Computer Communications Journal, Journal of C & EE, and International Journal of Communication Systems. Obaidat has served as the steering committee chair, advisory Committee Chair, honorary chair, and program chair of many international conferences. He is the founder of the International Symposium on Performance Evaluation of Computer and Telecommunication Systems, SPECTS and has served as the General Chair of SPECTS since its inception. Obaidat has received a recognition certificate from IEEE. Between 1994–1997, Obaidat has served as distinguished speaker/visitor of IEEE Computer Society. Since 1995 he has been serving as an ACM distinguished Lecturer. He is also and SCS Distinguished Lecturer. Prof. Obaidat is the founder of the SCS Distinguished Lecturer Program (DLP) and its present director. Between 1996 and 1999, Dr. Obaidat served as an IEEE/ACM program evaluator of the Computing Sciences Accreditation Board/Commission, CSAB/CSAC. Between 1995 and 2002, he has served as a member of the board of directors of the Society for Computer Simulation International. Between 2002 and 2004, He has served as Vice President of Conferences of the Society for Modeling and Simulation International SCS. Between

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2004-2006, he has served as Vice President of Membership of SCS. Prof. Obaidat is currently the Senior Vice President of SCS. He has been invited to lecture and give keynote speeches worldwide. His research interests are: wireless communications and networks, modeling and simulation, performance evaluation of computer systems, and telecommunications systems, security of computer and network systems, high performance computing/computers, applied neural networks and pattern recognition,

security of e-based systems, and speech processing. During the 2004/2005 academic, he was on sabbatical leave as Fulbright distinguished Professor and Advisor to the President of Philadelphia University (Dr. Adnan Badran who became in April 2005 the Prime Minster of Jordan. Prof. Obaidat is a Fellow of the Society for Modeling and Simulation International SCS, and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE).