1 Performance Analysis of the Distributed Coordination Function under Sporadic Traffic joint work with C.-F. Chiasserini (Politecnico di Torino) (Submitted for publication)

2 Motivation The bulk of literature on analytical models of considers only saturated sources Saturated conditions are not a desirable operating point for many applications, because of large queueing delays and/or packet losses We need to develop sound models to understand the behavior of networks under not-saturated conditions

3 Network scenario We consider n contending stations using the standard DCF mechanism of The MAC buffer of each station receives data packets according to an external, stationary arrival process of rate MAC buffers have finite capacity, equal to K packets Stations are within radio proximity of each other, there are no hidden terminals, no capture effects, … The communication channel is error-free

4 Our contribution We identify the critical assumptions in the development of an analytical model of the system We obtain an accurate model which is able to predict Network throughput Distribution of the MAC queue length Average packet delay Packet loss probability Our approach can account for: Burstiness in the arrival process of packets Variable packet sizes Transmission of multiple packets when a station seizes the channel (802.11e) Multirate environment (802.11b)

5 Saturated sources (Bianchi’s model) Description of the channel occupation: … … successful transmission idle slotcollision t  Discrete-time embedded Markov Chain

6 Basic model for saturated sources Embedded Markov Chain (simplified version of Bianchi’s model) probability that a (tagged) station sends out a packet at the beginning of an (arbitrary) time step = stage 0 stage 1 … stage m Independence assumption: The probability of successful transmission of a packet is computed as:

7 Numerical results for saturated sources Basic Access - CW min = 32 mod ns Aggregated packet throughput Number of Wireless Stations ( n ) RTS/CTS - CW min = 128 mod ns

8 Numerical results for saturated sources 1e-07 1e-06 1e Number of Wireless Stations mod sim b 0 sim b 1 sim b 2 sim b 3 sim b 4 sim b 5 Probability of states b i sim b 6

9 From the model solution we can compute The probability that a stations sends out a packet in an arbitrary step The probability that the station is backlogged (at least one packet in the queue) Modeling not-saturated sources First attempt: model “A” We incorporate in the description of the state of the tagged station the information of the number of packets in the queue: States: i = backoff stage j = packets in the queue # states = O(mK)

10 First attempt: model “A” Relying on the same independence assumption used for saturated sources, we can compute the collision probability, the successful probability, etc., and solve the system iteratively The model provides all performance metrics of interest (throughput, queue length distribution, queueing delay, packet loss probability, etc…) Note: the distribution of the number of backlogged stations is assumed to be binomial: ~ Binom e.g.: successful transmission probability:

11 Model A - numerical results Average number of packets in the queue Aggregated packet arrival rate (pkt/s), Λ mod A ns n = 10 stations – buffer size K = 20 – basic access scheme

12 Model A - numerical results Aggregated throughput (pkt/s) Aggregated packet arrival rate (pkt/s), Λ n = 10 stations – buffer size K = 20 – basic access scheme mod A ns mod A ns

13 Model A - numerical results Aggregated packet arrival rate (pkt/s), Λ n = 10 stations – buffer size K = 20 – basic access scheme mod A ns Average number of backlogged queues 650

14 Model A - numerical results Number of backlogged stations n = 10 stations – buffer size K = 20 – basic access scheme pdf Λ = 650 pkt/s mod A ns Binomial Not binomial !

15 Model A - conclusions The independence assumption among stations does not hold in networks under not-saturated conditions  it is not possible to just analyze the behavior of a tagged station in isolation This fact has been neglected by most analytical approaches proposed so far in the literature: e.g.: O. Tickoo and B. Sikdar, ``Queueing Analysis and Delay Mitigation in IEEE Random Access MAC based Wireless Networks,'‘ INFOCOM 2004, Hong Kong, China, March Note: the independence assumption would indeed hold in a hypothetical system in which

16 We compute transmission probabilities, collision probabilities, etc, conditioned to the number C of backlogged queues in the system) Modeling not-saturated sources Second attempt: model “B” We enrich the description of the tagged station with the number of backlogged queues (belonging to other stations): States: i = backoff stage j = packets in the queue # states = O(mKn) k = backlogged queues e.g. = P { send out a packet | c backlogged queues }

17 Model B - numerical results Average number of packets in the queue Aggregated packet arrival rate (pkt/s), Λ n = 10 stations – buffer size K = 20 – basic access scheme mod B ns

18 Model B - numerical results Aggregated packet arrival rate (pkt/s), Λ n = 10 stations – buffer size K = 20 – basic access scheme Average number of backlogged queues mod B ns

19 Model B - numerical results Number of packets in the queue n = 10 stations – buffer size K = 20 – basic access scheme pdf mod B ns - Λ = 720 ns - Λ = 640

20 Model B - numerical results Number of backlogged stations n = 10 stations – buffer size K = 20 – basic access scheme pdf ns - Λ = 640 ns - Λ = 550 mod B

21 Impact of bursty traffic n = 5 stations – buffer size K = 40 – basic access scheme

22 Multi-rate multi-hop environment Assumptions: All nodes can hear each other (no hidden nodes, etc…) Stations can choose their data sending rate (2 or 11 Mb/s) Error free channel (within transmission range, no matter the distance) Dilemma: In terms of overall network performance, it is better to make a single hop at low rate, or two hops at high rate ? AB C 2 Mb/s 11 Mb/s

23 Multi-rate multi-hop environment Number of stations at 2 Mb/s mod ns bytes ns bytes ns bytes ns bytes Total number of stations = 20 (basic access scheme) (saturated case) Aggregated data throughput (Mb/s) 3.1 Mb/s 5.5 * (1 – 4/20) = 4.4 Mb/s 1.3 Mb/s 2 * (1 – 8/20) = 1.2 Mb/s

24 Aggregated data throughput (Mb/s) Multi-rate multi-hop environment (saturated case) Total number of stations = 20 (RTS/CTS scheme) mod ns bytes ns bytes ns bytes ns bytes Number of stations at 2 Mb/s Region where best choice is two-hops at 11 Mb/s

25 The optimal choice of data rate jointly depends on: Access scheme (basic or RTS/CTS) Payload size Fraction of stations switching from 11 to 2 Mb/s … and on Physical and MAC layer parameters Multi-rate multi-hop environment (saturated case)

26 Multi-rate multi-hop environment (not saturated case) mod ns - n_low = 0 ns - n_low = 1 ns - n_low = 2 ns - n_low = 3 ns - n_low = 4 Average queueing delay (ms) Number of stations at 11 Mb/s Variable number of stations, each generating 50 pkt/s

27 Power consumption (saturated conditions) Number of Wireles Stations Average Power Consumption (W) mod - RTS/CTS ns - RTS/CTS mod - basic ns - basic P_tx = 1.65 W – P_overhearing = 1.4 W – P_idle = 1.15 W

28 Power consumption (non-saturated conditions) Aggregated packet arrival rate (pkt/s), Λ Average Power Consumption (W) n = 10 stations – buffer size K = 20 ns - RTS/CTS mod - basic ns - basic mod - RTS/CTS

29 Final remarks We have found an accurate analytical model with O( mKn ) states Es: m = 7, K = 20, n = 10  1400 states The behavior of stations is highly correlated  independence assumption does not hold The key point is modeling the number of competing (backlogged) stations Model limitation: we analyze only a symmetrical system ( i = )

30 The End Thanks for your attention questions & comments…