Performance Analysis of Aloha-based MAC Protocols for Optical WDM Networks
Goran Đambić, Alen Bažant
system complexity are reduced since tunable receivers are Abstract—Star and ring are the two most frequent used not needed. 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 II. OPTICAL COMPONENTS 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 Many efforts have been done in research and development of buffer in every node. of WDM networks because of two reasons: first, the bandwidth of current fiber installations can be greatly Index Terms—optics, wavelength division multiplexing, media enhanced, and second, the speed mismatch between optical access control protocols, aloha, performance, star topology and electronical components can be circumvented because instead of one very fast channel, there are multiple slower channels. I. 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 Fig. 1: Network architecture 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 There are two classes of WDM networks – wavelength other nodes, so the destination node will select traffic routing networks and broadcast-and-select networks, which headed for him, while the other nodes will discard it. is studied in this work. Our network consists of M nodes Single-hop means that every node is able to address and equipped with one tunable transmitter and one fixed send packet to any other node directly. That capability is receiver. Our network uses C channels, each represented by achieved by having transmitters tunable over all used one distinct wavelength. This work is not concerned with wavelengths. physical characteristics of the network – the choice of laser Media Access Protocols designed for optical WDM for the transmitter, the channel spacing between networks can be classified as either reservation or pre- wavelengths, the channel selectivity of the receiver and allocation protocols [1], [2]. Reservation protocols mostly other characteristics are assumed to be sufficiently chosen use one control channel (although some don't) to reserve for WDM star topology network. access on all other channels. Pre-allocation protocols The topology of our network is shown in Fig. 1. 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 the processing time of destination node. The packet delay is III. INTERLEAVED SLOTTED ALOHA PROTOCOL defined as the time between generation of the packet and it's reception by the destination node, and is also normalized to Interleaved Slotted Aloha protocol (I-SA) examined in this packet transmission time. There are few assumptions for work is based on the network where channels are pre- this model [2]: allocated for data-reception. A source node must first tune its tunable transmitter to the home channel of the 1. nodes are identical, destination node and then waits for the beginning of the 2. in every node, packet generation is a Poisson new slot to transmit a packet. A node receives all traffic on process with rate λ, his home channel. Packets intended for the node are 3. a packet generated at any node has equal accepted, and the others are discarded. If there is M = C, probability of being directed to any other node, then all packets on node's home channel are sent for the except for itself, node. 4. per slot, only one packet can be generated in every If a node wants to transmit a packet to another node, it must node, first determine the home channel of the other node. That 5. at most B packets can be queued at the node can be achieved without any global tables, since the (without the one being in process of transmission), destination node numbers, C and M are known at all times. 6. all packets are fixed in length.
Node mi is assigned ci as its home channel for reception based on The receiver can be in one of the two states: idle – the c = m mod C receiver is not receiving a packet, and receiving – the node i i is receiving a packet. The receiver never initiates activity, so it will not be included in the model. where ci is element of {0, 1, 2, ..., C-1} and 0 ≤ i ≤ M - 1. In our network, the source node is tuned to his own home The transmitter initiates activity and can be in on of the channel, so it cannot find out if the packet successfully states shown in Fig. 2. 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 Fig. 2: State diagram of I-SA for B = 1 backoff state. In that state, the transmitter decides if it will retransmit in the next slot based on the backoff probability Possible states for transmitter are: idle – there is no Pb. The retransmission can be attempted in the next slot generated packet in the node, transmitting – transmitting (Immediate First Retransmission – IFRT) or after a one slot the packet, and backoff – the collision has occurred and the of pause (Delayed First Retransmission). The protocol used transmitter will transmit in the next slot with probability of in this study is based on IFRT approach. If the Pb. retransmission succeeds, it transmits the next packet in the The probability of a transition from state Si to Sj is denoted queue (if there is one). If not, it stays in the backoff state. as p[i,j]. The τi 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 IV. MODEL FOR PERFORMANCE ANALYSIS generated. States Si, where 1 ≤ i ≤ B+1, are transmit states. The transition from transmit states depends on whether the I-SA protocol described in section III is analyzed through packet was successfully transmitted and whether a new semi-markov model. This model will be reduced to markov packet is generated. The probabilities are given in Fig. 2. chain because the sojourn time of every state is 1. The queue is full in state SB+1 and S2(B+1) and packet In this work we will consider network throughput and generation is blocked. packet delay. The throughput is expressed as packets per States S(B+1)+i, where 1 ≤ i ≤ B+1, are backoff states. The unit time, where time is normalized to the packet transition from backoff states depends on Pb and on transmission time, which includes propagation delay and generation of a new packet. Limiting probabilities of being in state Si of embedded V. ANALYZING MODEL markov chain are denoted as Vi and can be calculated from transition probability matrix shown in Fig. 3. 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 1-β β 0 0 0 relation of throughput and packet delay to packet generation P (1-β) P β 0 (1-P )(1-β) (1-P )β s s s s rate, number of nodes and number of channels. In every P= 0 P 0 0 1-P s s scenario we assumed the same probability of leaving the 0 P (1-β) P β (1-P )(1-β) (1-P )β backoff state Pb = 0.05. b b b b 0 0 P 0 1-P b b Fig. 3: Transition probability matrix for B = 1 A. Network with single channel Because of sojourn times are equal to 1, the limiting Fig. 4 shows a network throughput when there is C = 1, probabilities of being in state Si of semi-markov process are B = 1 and M is from {4, 8, 16, 32, 64}, and Fig. 5. has the Pi = Vi. same C and M, but with B ten times greater, The probability of successful transmission Ps depends on the limiting probabilities of the process being in one of the B = 10. transmit states, as shown in [2]:
M 1 P1 P2 P3 ... PB1 Ps = 1 C
Since Ps depends on Pi and Pi depends on Ps, the following algorithm can be used in calculation:
1. choose any value for Ps, 2. compute Pi for that Ps, 3. compute new Ps with computed Pi, 4. 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 Fig. 4: Throughput of I-SA for system with one channel and buffer of size 1 transmits packets when in any of the states Si, where 1 ≤ i ≤ 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:
EN D = (P1 ... PB1 )Ps
Fig.5: Throughput of I-SA for system with one channel and buffer of where E[N] is the average number of packets in node, size 10 which is As mentioned before, network throughput is defined as E[N] = E[N ]P + ... + E[N ]P 0 0 2(B + 1) 2(B+1) number of packets successfully transmitted per slot over all data channels. It is primarily dependent on two parameters: and E[N ] = 0, E[N ] = E[N ] = i, for all 1 ≤ i ≤ B+1. 0 i (B+1)+i collisions and number of nodes. Fig. 4 and Fig. 5 clearly show that the size of buffer doesn't following subsection will show how does the number of play any significant role in network throughput. channels affect the performance. 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 B. Networks with multiple channels the nodes, the collisions begin to happen more and more often and even for small-generated traffic the throughput is Fig. 8 and Fig. 9 show the network throughput when the low. For example, for λ = 0.40, if there are M = 16 nodes, number of channel increases from 1 to a value from interval the network throughput is around S = 0.37. But if we {M, M/2, M/4}. increase the number of nodes to M = 64 the throughput falls down to only S = 0.13.
Fig. 8: Throughput of I-SA system with varying number of channels and buffer of size 1 Fig. 6: Packet delay of I-SA for system with one channel and buffer of size 1
Fig. 9: Throughput of I-SA system with varying number of channels and buffer of size 10 Fig. 7: Packet delay of I-SA for system with one channel 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 Fig. 6 and Fig. 7 show the packet delay for the same we look in Fig. 4, we will see that the network throughput is parameters. Again, the size of the buffer doesn't affect the S = 0.13 for M = 64 nodes and λ = 0.40. If we find the same delay. value in Fig. 8, we will find out that it has increased to It is visible from both pictures that as the number of nodes S = 9.1, for C = M = 64, which is a significant increase. increases, the packet delay is greater. The reason for that is Also, it is visible that the throughput is growing slowly as that every node spends more time retransmitting the packet, we increase the buffer size, which is noticeable only in because the network is congested and the probability of networks with 32 or more nodes. 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 VII. 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 Fig. 10: Packet delay of I-SA system with varying number of channels and buffer of size 1 will suffer even if ratio M/C = 1.
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