ࡱ>   `|bjbj 2c@ ~ R%R%R%8%<%TI:&&(N&N&N&N&'''8888888$:hg=8)y'"'))8 N&N&+9.,,,)~ pN&N&8,)8,,7|*7 N&& |X1R%*7 8| :<I:7Z=3,(=$7=7$'>',,($)('''88[,d'''I:))))R%R%   Performance Analysis of Aloha-based MAC Protocols for Optical WDM Networks Goran ambi, Alen Ba~ant Abstract Star and ring are the two most frequent used topologies for optical networks, due to their superior power loss compared to bus and hybrid networks. In this work we will focus our attention to Slotted Aloha-based media access control protocol designed for star-coupled networks. We will analyze performance for this protocol, with variations in number of the nodes, the number of the channels and the size of buffer in every node. Index Termsoptics, wavelength division multiplexing, media access control protocols, aloha, performance, star topology Introduction This work uses an analytical model based on Markov chains introduced in [1], [2], [3], [4], [5], [6], [7], [8], [9] for performance evaluation of Aloha-derived Media Access Control protocols in optical networks based on Wavelength Division Multiplexing (WDM). Wavelength Division Multiplexing means that there is more than one channel simultaneously in use, so traditional single-channel Aloha-based protocols had to be adapted. Specifically, we analyze WDM-based, star-coupled, broadcast-and-select single-hop Metropolitan Area Networks (MAN) based on a wavelength-insensitive passive star coupler (PSC). Broadcast-and-select means that PSC will collect all wavelengths from one node and will broadcast them to all other nodes, so the destination node will select traffic headed for him, while the other nodes will discard it. Single-hop means that every node is able to address and send packet to any other node directly. That capability is achieved by having transmitters tunable over all used wavelengths. Media Access Protocols designed for optical WDM networks can be classified as either reservation or pre-allocation protocols [1], [2]. Reservation protocols mostly use one control channel (although some don't) to reserve access on all other channels. Pre-allocation protocols preassign wavelengths to nodes, where each node has dedicated home-channel for transmission or reception. Pre-allocation protocols are generally less complex and simpler than reservation protocols. Pre-allocation protocols can be further classified as random or static. Both random and static pre-allocation protocols have been developed for nodes with either tunable transmitter and fixed receiver or fixed transmitter and tunable receiver. In this work we will consider nodes equipped with one fixed receiver and one tunable transmitter, which means that every node has dedicated home-channel for data reception. System cost and system complexity are reduced since tunable receivers are not needed. Optical components Many efforts have been done in research and development of WDM networks because of two reasons: first, the bandwidth of current fiber installations can be greatly enhanced, and second, the speed mismatch between optical and electronical components can be circumvented because instead of one very fast channel, there are multiple slower channels.  Fig. 1: Network architecture There are two classes of WDM networks wavelength routing networks and broadcast-and-select networks, which is studied in this work. Our network consists of M nodes equipped with one tunable transmitter and one fixed receiver. Our network uses C channels, each represented by one distinct wavelength. This work is not concerned with physical characteristics of the network the choice of laser for the transmitter, the channel spacing between wavelengths, the channel selectivity of the receiver and other characteristics are assumed to be sufficiently chosen for WDM star topology network. The topology of our network is shown in Fig. 1. Interleaved Slotted Aloha protocol Interleaved Slotted Aloha protocol (I-SA) examined in this work is based on the network where channels are pre-allocated for data-reception. A source node must first tune its tunable transmitter to the home channel of the destination node and then waits for the beginning of the new slot to transmit a packet. A node receives all traffic on his home channel. Packets intended for the node are accepted, and the others are discarded. If there is M = C, then all packets on node's home channel are sent for the node. If a node wants to transmit a packet to another node, it must first determine the home channel of the other node. That can be achieved without any global tables, since the destination node numbers, C and M are known at all times. Node mi is assigned ci as its home channel for reception based on ci = mi mod C where ci is element of {0, 1, 2, ..., C-1} and 0 d" i d" M - 1. In our network, the source node is tuned to his own home channel, so it cannot find out if the packet successfully arrived at the destination or the collision has occurred. There are few ways to assure reception of the sent packet. In our network, we choose to extend the slot and cut it in two phases in phase one, the source node tunes its transmitter to destination's home channel and transmits the packet. In phase two, the destination node decodes the packet header, verifies the CRC, tunes its transmitter to home channel of the source node and transmits the acknowledgement. If M = C, then the acknowledgement packet is always received. If M > C, the acknowledgement packet can collide with another packet on the same channel, so the phase two must me further subslotted. A source node knows that a collision has occurred if it does not receive the acknowledgement packet. If a collision did occur, the transmitting node goes to backoff state. In that state, the transmitter decides if it will retransmit in the next slot based on the backoff probability Pb. The retransmission can be attempted in the next slot (Immediate First Retransmission IFRT) or after a one slot of pause (Delayed First Retransmission). The protocol used in this study is based on IFRT approach. If the retransmission succeeds, it transmits the next packet in the queue (if there is one). If not, it stays in the backoff state. model for performance analysis I-SA protocol described in section III is analyzed through semi-markov model. This model will be reduced to markov chain because the sojourn time of every state is 1. In this work we will consider network throughput and packet delay. The throughput is expressed as packets per unit time, where time is normalized to the packet transmission time, which includes propagation delay and the processing time of destination node. The packet delay is defined as the time between generation of the packet and it's reception by the destination node, and is also normalized to packet transmission time. There are few assumptions for this model [2]: nodes are identical, in every node, packet generation is a Poisson process with rate , a packet generated at any node has equal probability of being directed to any other node, except for itself, per slot, only one packet can be generated in every node, at most B packets can be queued at the node (without the one being in process of transmission), all packets are fixed in length. The receiver can be in one of the two states: idle the receiver is not receiving a packet, and receiving the node is receiving a packet. The receiver never initiates activity, so it will not be included in the model. The transmitter initiates activity and can be in on of the states shown in Fig. 2.  Fig. 2: State diagram of I-SA for B = 1 Possible states for transmitter are: idle there is no generated packet in the node, transmitting transmitting the packet, and backoff  the collision has occurred and the transmitter will transmit in the next slot with probability of Pb. The probability of a transition from state Si to Sj is denoted as p[i,j]. The i is average sojourn time of state Si and is always equal to 1. The transmitter will leave S0 and go to S1 if a new packet is generated. States Si, where 1 d" i d" B+1, are transmit states. The transition from transmit states depends on whether the packet was successfully transmitted and whether a new packet is generated. The probabilities are given in Fig. 2. The queue is full in state SB+1 and S2(B+1) and packet generation is blocked. States S(B+1)+i, where 1 d" i d" B+1, are backoff states. The transition from backoff states depends on Pb and on generation of a new packet. Limiting probabilities of being in state Si of embedded markov chain are denoted as Vi and can be calculated from transition probability matrix shown in Fig. 3.  P= Fig. 3: Transition probability matrix for B = 1 Because of sojourn times are equal to 1, the limiting probabilities of being in state Si of semi-markov process are Pi = Vi. The probability of successful transmission Ps depends on the limiting probabilities of the process being in one of the transmit states, as shown in [2]: Ps =  EMBED Equation.3  Since Ps depends on Pi and Pi depends on Ps, the following algorithm can be used in calculation: choose any value for Ps, compute Pi for that Ps, compute new Ps with computed Pi, repeat steps 2 and 3 until Pi converges. Channel utilization for a node is the percent of the time node spends transmitting packet. Network throughput is defined as channel utilization of all C channels. A node transmits packets when in any of the states Si, where 1 d" i d" B+1. The number of packets transmitted by node can be calculated from probabilities of being in one of those states and probability of successful transmission Ps. The throughput for the network is S = M Ps (P1 + ... + PB+1) The packet delay is defined as a time from a packet creation until its reception at destination. That time include waiting for the beginning of the next slot, backoff time (if a collision occurs), and packet transmission time. The packet delay can be calculated by applying Little's Law: D =  EMBED Equation.3  where E[N] is the average number of packets in node, which is E[N] = E[N0]P0 + ... + E[N2(B + 1)]P2(B+1) and E[N0] = 0, E[Ni] = E[N(B+1)+i] = i, for all 1 d" i d" B+1. Analyzing model The model from section IV was used to analyze throughput and packet delay. The analysis was performed using Matlab. The purpose of the analysis was to show the relation of throughput and packet delay to packet generation rate, number of nodes and number of channels. In every scenario we assumed the same probability of leaving the backoff state Pb = 0.05. Network with single channel Fig. 4 shows a network throughput when there is C = 1, B = 1 and M is from {4, 8, 16, 32, 64}, and Fig. 5. has the same C and M, but with B ten times greater, B = 10.  Fig. 4: Throughput of I-SA for system with one channel and buffer of size 1  Fig.5: Throughput of I-SA for system with one channel and buffer of size 10 As mentioned before, network throughput is defined as number of packets successfully transmitted per slot over all data channels. It is primarily dependent on two parameters: collisions and number of nodes. Fig. 4 and Fig. 5 clearly show that the size of buffer doesn't play any significant role in network throughput. It is also visible that up to a point, the throughput grows with the growth of packet generation rate and number of nodes. After that point, if we keep increasing the number of the nodes, the collisions begin to happen more and more often and even for small-generated traffic the throughput is low. For example, for  = 0.40, if there are M = 16 nodes, the network throughput is around S = 0.37. But if we increase the number of nodes to M = 64 the throughput falls down to only S = 0.13.  Fig. 6: Packet delay of I-SA for system with one channel and buffer of size 1  Fig. 7: Packet delay of I-SA for system with one channel and buffer of size 10 Fig. 6 and Fig. 7 show the packet delay for the same parameters. Again, the size of the buffer doesn't affect the delay. It is visible from both pictures that as the number of nodes increases, the packet delay is greater. The reason for that is that every node spends more time retransmitting the packet, because the network is congested and the probability of successfully transmitted packet is very low. The above analysis shows that I-SA protocol with one channel is unacceptable in real-life networks and that even increase in buffer size doesn't make any difference. The following subsection will show how does the number of channels affect the performance. Networks with multiple channels Fig. 8 and Fig. 9 show the network throughput when the number of channel increases from 1 to a value from interval {M, M/2, M/4}.  Fig. 8: Throughput of I-SA system with varying number of channels and buffer of size 1  Fig. 9: Throughput of I-SA system with varying number of channels and buffer of size 10 It is obvious that any increase in number of channels from 1 results in dramatically greater throughput. For example, if we look in Fig. 4, we will see that the network throughput is S = 0.13 for M = 64 nodes and  = 0.40. If we find the same value in Fig. 8, we will find out that it has increased to S = 9.1, for C = M = 64, which is a significant increase. Also, it is visible that the throughput is growing slowly as we increase the buffer size, which is noticeable only in networks with 32 or more nodes.  Fig. 10: Packet delay of I-SA system with varying number of channels and buffer of size 1  Fig. 11: Packet delay of I-SA system with varying number of channels and buffer of size 10 Considering the packet delay shown in Fig. 10 and Fig. 11, it is noticeable that it decreases as the number of channels grows, almost insensitive to the number of nodes. From those figures, we derive a conclusion that as long as the ratio M/C )  *\]`ahino "cdgh@!A!B!!!d'f'Z(_(((])^)_)))úhY6CJ] hYCJj hYU hY5\hYmHsHhY6H*]jhYU hY6] hY6hYI  hi|}Iyz$a$$a$$a$yy|. """"f#>%?%T%&&T' (+(,( )\)])_)))*,$ & Fa$$a$))))))*"****J+L+N+V+X+Z++++++H,J,L,b,d,f,,,,,,......///>/@////506070`0a0b000000000>1?1@1\1]1^1a1b1c1111øhY5\mHsHhYmHsHjhYUmHnHtH u hYH*hY6H*] hY6] hY5\hY hYCJH,/ 0000000000e11122~2222222$ & Fa$$a$E& #$+D-D/M $a$1122222222#2$2%21222328292:2F2G2H2222222222222222222233333444 4 44J5L5N5555555555555µµµµhY6H*]aJmH sH hY6]aJmH sH hYaJmH sH jN#hYEHUjE hYUVnH tH jhYUhY6H*] hY6]hYB25555 7 7(7)7g7h77786888::::J;K;M;;;;;$a$$a$ 5$7$8$9DH$5 7 777$7%7&7'7/737h7l7o7r7s7u7v777777777777777777 88v:x:y:z:::::::;;; ;+;,;A;B;K;L;M;;;;;;>>T?V???@@jJhYU hYCJj(hYU hYH*hY6H*]j)&hYEHUj&E hYUVnH tH jhYU hY6]hYF;;<(=@@@b@c@e@@@/ALBMCNCnCoCCCCKDLDNDDD(G$a$$a$$a$@@@@L@c@d@e@@CCCCCCCCCKDLDMDNDD^E_EkElEFFFFFFFG(G*H+H,HHHHHHI IIIIIdeeef&f(fPf(j)j*j+j1j߫hY6]aJmH sH Uh%kijJhYUjhYUhYaJmH sH h0jhYUjthYU hY6]jhYU hYCJjkhYUhY>(G*H,HHHHHH6fNfPf1j2j3j>j?jkF & FEƀ:Z[]$a$$a$$a$ 5$7$8$9DH$ is maintained, the packet delay will remain almost the same. That is a very important characteristic of I-SA protocol. For example, there will be a 65% decrease in packet delay and a 100% increase in system throughput if we increase the number of channels from M/4 to M, at  = 0.30 and M = 32. Conclusion This works used mathematical model based on semi-markov process to analyze the behavior and performance of media access control protocol based on Slotted Aloha. It was shown that the main parameter for the performance is a ratio of number of the nodes and number of the channels. The increase in number of nodes creates more traffic and that means more collisions occur that affects performance. But if there is also a matching increase in the number of channels, the traffic distributes to more wavelengths and the number of collisions falls down, which results in retained level of performance. That means that I-SA protocol is a good choice for networks when the traffic is low or medium. Still, when the traffic is heavy, the performance will suffer even if ratio M/C = 1. REFERENCES Krishna M. Sivalingam, Kalyani Bogineni, Patrick W. Dowd, Pre-Allocation Media Access Control Protocols for Multiple Access WDM Photonic Networks, in Proc. ACM SIGCOMM '92, pp. 235-246, Aug. 1992. Kalyani Bogineni, Patrick W. Dowd, Analytical Modeling of WDM Media Access Protocols, Proceedings of the 26th Hawaii International Conference, vol. 1, pp. 266 275, 1993. Krishna M. Sivalingam, Patrick W. Dowd, Latency Hiding Strategies of Pre-Allocation Based Media Access Control Protocols for WDM Photonic Networks, in Proc. 26th Simulation Symposium, March 1993. Patrick W. Dowd, Kalyani Bogineni, A Modeling Technique for Media Access Protocol Evaluation, Mascots, pp. 115 120, 1993. Patrick W. Dowd, Kalyani Bogineni, TDM-based WDM access protocols: A comparison of Reservation and Pre-allocation Strategies for a Photonic Star-Coupled Configuration, Int. Journal in Computer Simulation 4, pp. 21 40, 1994. Krishna M. Sivalingam, K. Bogineni, Patrick W. Dowd, Acknowledgement Techniques of Random Access Based Media Access Protocols for a WDM Photonic Environment, IPC Science and Technology Press Kalyani Bogineni, Krishna M. Sivalingam, Patrick W. Dowd, Low Complexity Multiple Access Protocols for Wavelength Division Multiplexed Photonic Networks Kalyani Bogineni, Patrick W. Dowd, A Collisionless Multiple Access Protocol for a Wavelength Division Multiplexed Star-Coupled Configuration: Architecture and Performance Analysis1j3j4j=j?jzjjk(kYkpkrkkkClPlRltlulllllmmmm npnnnn+oOooxvxxxxyyyyyyyyyyyyz||||||$|&|(|׬'hY6H*]^JaJmHnH sHtH $hY6]^JaJmHnH sHtH hY^JaJmHnH sHtH jhYUU hYH*] hY] hY6hYCJmH sH hYmH sH hY<kkullq*F & FEƀ:Z[]F & FEƀ:Z[]F & FEƀ:Z[]lmn,oq*F & FEƀ:Z[]F & FEƀ:Z[]F & FEƀ:Z[], IEEE Journal on Lightwave Technology, vol. 10, Nov. 1992. Patrick W. 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