Optimal Selection of Power Saving Classes in IEEE e Lei Kong, Danny H.K. Tsang Department of Electronic and Computer Engineering Hong Kong University of Science and Technology IEEE Wireless Communication & Network Conference ( WCNC 2007 )

Outline Introduction Proposed Algorithm – System model – Cost metric and Delay metric – Policy Optimization Simulation Conclusion

Introduction According to the mobility extension, – IEEE e defines the sleep mode operation for the power saving which is one of the most important features for MSSs to extend their lifetime. In order to support different service connections – IEEE e offers several sleep mode types, called Power Saving Classes (PSCs)

Introduction – e sleep mode operations Power Saving Class of Type I Power Saving Class of Type II Power Saving Class of Type III … T S_init (Initial sleep window) 2 x T S_init TLTL 4 x T S_init T S_max Incoming packet TLTL TSTS Incoming packets … TSTS normal operation sleep windows listening windows MOB_TRF-IND

Relative Work Sleep mode in IEEE e has been generally recognized as effective in discontinuous reception. However, their model only applies for PSCs of type I and does not capture the new characteristics of PSCs of type II.

Relative Work Lei Kong and Danny H. K. Tsang, “Performance Study of Power Saving Classes of Type I and II in IEEE e”, To appear in the Proc. of of the 31st IEEE Conference on Local Computer Networks, Tampa, Florida, US, November – The original models have captured the inherent properties of two PSCs accurately and also show the energy delay trade-offs on different PSCs

Motivation The static timeout policy may solve the problem of when to perform the sleep mode switching, but it cannot resolve the issue on PSCs selection.

Goal Our main goal is to find the optimal selection for PSC of types that achieves the minimum energy cost or traffic delay under different traffic requirements.

Assumptions We assume that packet arrival rate λ ( packets/frame ). We also denote μ ( packets/frame ) as the service rate between BS and MSS. In PSC of type I, we assume the energy for device to switch on and off in T L is negligible

Assumptions In PSC of type II, we assume that MSS would remain in sleep mode if the arriving packets from the pervious sleep interval is less than or equal to the maximum number of packets that it could transmit during T L. TLTL TSTS Incoming packets

System model Definitions – I = { S N, S I, S II } representing normal mode, sleep mode of type I and type II – A = { s_N, s_I, s_II } with the intuitive meaning of ”switching to normal mode”, ”switching to type I” and ”switching to type II”, respectively – S I (k) represent the multi-sleep state of type I, where 0 ≤ k ≤ w and w is the final sleep stage – P k is the probability that there is packet arrival at BS in sleep stage S I (k) – Q is the transition probability that PSC of type II to normal mode – R i is a decision epoch in state i

System model

Examples s_N Stay On Normal mode The next decision takes place when the system endures a busy period and becomes idle again.

Examples s_I Switch to PSC I The next decision takes place when the system endures normal mode and becomes sleep mode again.

Examples s_II Switch to PSC II The next decision takes place when the system endures normal mode and becomes sleep mode again.

Cost metric and Delay metric Definition – τ i (a) = the expected time duration until the next decision epoch if action a is chosen in state i. – c i (a) = the expected power consumption incurred until the next decision epoch if action a is chosen in state i. – d i (a) = the expected packet delay if action a is chosen in the present state i Goal

Cost metric and Delay metric Definitions – Denote P B, P I, P S, P L as the power consumption level of busy period B, idle period I, sleep interval and listen interval T L, respectively. – E [B], E [I] is means busy period duration and idle period duration – S is the random variable of service time for each packet and E [S] = 1 /μ

Cost and Delay in Normal mode Expected time duration for normal mode Expected power consumption for normal mode

The mean waiting time for the packet – E[W] is the mean waiting time for the packet arrival during the busy period. – ρ=λ/μ is traffic intensity – E[R] = E[S 2 ]/(2E[S]) is the residual processing time – According to Pollaczek-Khintchine(PK-) mean value formula [5], E[W] is Cost and Delay in Normal mode

Expected packet delay for Normal mode

Cost and Delay in PSC I Packet arrival Probability for PSC I – P k is the probability that there is packet arrival at BS in sleep stage S I (k)

Cost and Delay in PSC I The Vacation time and busy period for PSC I – V k is the vacation time (i.e. the sleep window size plus the listen interval) at stage k – is the mean time of exceptional busy period to transmit previously buffered traffic accumulated in sleep stage k and can be derived from the following equation:

Cost and Delay in PSC I Expected time duration until vacations k – is the expected duration until the next decision epoch after sleeping for k vacations

Cost and Delay in PSC I Expected time duration for PSC I

Cost and Delay in PSC I Expected Power consumption until vacations k – is the total expected energy consumption when system wakes up after k vacation cycles and becomes idle. – ε i = P S 2 i T 0 + P L T L is the power consumption at the sleep stage i

Cost and Delay in PSC I Expected Power consumption for PSC I – E sw denotes the power consumption in switch-on and switch-off the transceiver at physical layer.

Cost and Delay in PSC I Expected packet delay for PSC I – is the total expected packet delay when system wakes up after k vacation cycles. ρ=λ/μ is traffic intensity

Cost and Delay in PSC II Packet arrival Probability for PSC II – V II is the vacation time for PSC of type II (i.e. the sleep window size plus the listen interval) – d is maximum number of packets that it could transmit during T L – (1 − Q) is the transition probability that MSS keeps in state S II

Cost and Delay in PSC II Expected time duration for PSC II

Cost and Delay in PSC II Expected power consumption for PSC II

Cost and Delay in PSC II Expected packet delay for Type II

Policy Optimization Let x i (a) are the expected number of times that the system is in state i and command a is issued. We define in our model that every decision epoch only takes place as soon as MSS becomes idle in S N. In other words, x i (a) = 0, ∀ a and i ∈ {S I, S II }.

Policy Optimization We formulate two probabilistic constrained optimization problems: – power optimization under delay constraint maximal expected delay with a upper bound δ.

Policy Optimization – delay optimization under power constraint meaning that the battery life time would be extended σ times in the long run

Simulation P B = 750mW, P I = P L = 170mW and P s = 50mW, and for switching cost E sw = 1.5J

Simulation A. Cost Metric Comparison

Simulation B. The Space of Optimal Policies (delay 20 frame)

Simulation B. The Space of Optimal Policies (delay one frame)

Conclusion In this paper, we propose a semi-Markov Decision Processes (Semi-MDP) method into the sleep mode operation in IEEE e. We find out the optimal selection for PSC and efficiently under different traffic conditions that minimize energy consumption for MSS