Vineeth Bala Sukumaran

Tradeoff of average power and average delay for a point-to-point link with fading

We consider a discrete time system with packets arriving randomly at rate λ per slot to a fading point-to-point link, for which the transmitter can control the number of packets served in a slot by varying the transmit power. We provide an asymptotic characterization of the minimum average delay of the packets, when average transmitter power is a small positive quantity V more than the minimum average power required for queue stability. We show that the minimum average delay will grow either as log(1/V ) or 1/V when V ↓ 0, for certain sets of values of λ. These sets are determined by the distribution of fading gain, the maximum number of packets which can be transmitted in a slot, and the assumed transmit power function, as a function of the fading gain and the number of packets transmitted. We identify a case where the above behaviour of the tradeoff differs from that obtained from a previously considered model, in which the random queue length process is assumed to evolve on the non-negative real line.

Tradeoff of average service cost and average delay for the state dependent M/M/1 queue

The optimal tradeoff between average service cost rate and average delay, is addressed for a M/M/1 queueing model with queue-length dependent service rates, chosen from a finite set. We provide an asymptotic characterization of the minimum average delay, when the average service cost rate is a small positive quantity V more than the minimum average service cost rate required for stability. We show that depending on the value of the arrival rate, the assumed service cost rate function, and the possible values of the service rates, the minimum average delay either a) increases only to a finite value, b) increases without bound as log (1 over V, or c) increases without bound as 1 over V, when V ↓ 0. We apply the analysis to a flow-level resource allocation model for a wireless downlink. We also investigate the asymptotic tradeoff for a sequence of policies which are obtained from an approximate fluid model for the M/M/1 queue.

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Stability and delay analysis of delay tolerant networks with random message arrivals

We study stability and average delay in single-source single-destination delay tolerant networks with random message arrivals. In particular, we analyze source spray-and-wait routing protocol without feedback. We obtain conditions on arrival rate under which the source queue is stable. We show that the maximum supported arrival rate is linearly proportional to the number of relays and inversely proportional to the spray-and-wait parameter. Further, we obtain an approximate expression for the average queueing delay. We show that it increases with the spray-and-wait parameter. Through simulations, we show that the average delivery delay and average end-to-end delay first decreases and then increases with the spray-and-wait parameter. We also validate our analytical findings through simulations.

Bayesian Quickest Change Detection for Active Sensors

We consider the energy efficient quickest change detection problem for active sensors, which use radar, ultrasound, or optical sensing to control the information content in the sequentially collected noisy data. Controlling the extent of information contained in the collected data would lead to a cost or energy expenditure, where the cost would naturally increase as the extent of contained information increases. For such a sensor, our objective is to design control policies that optimally trade off performance metrics, such as detection delay, average cost expended in control, and probability of false alarm. We consider this problem in the setting of Bayesian quickest change detection. We propose two simple heuristic threshold policies, for which the total cost is shown to be close to the optimal through simulations and numerical studies.

On power-law decay exponents and Barabasi models for subscriber usage behaviour in mobile networks

We consider whether Barabási multiclass priority service queueing models are appropriate for modelling voice and short message service interusage and voice usage residual time distributions for a set of high usage subscribers of an Asian telecommunication service provider. We find that a model with a non priority service discipline rather than any priority discipline provides an alternative explanation for the fitted power-law for the interusage time distributions. We also find that a Barabási model provides an alternative explanation to the fitted power-law for the voice usage residual time distribution. However, the exponent of the fitted power-law has not been observed before. Therefore, we propose and analyse a new Barabási list-of-tasks priority model with time varying and discrete task priorities. For a special case we show that the waiting time distribution has a power-law with a previously unknown power-law decay exponent, which is different from the observed exponent for the voice usage residual time distribution.

Delay optimal scheduling of a discrete-time batch service queue for point-to-point channel code rate selection

We consider the problem of characterizing the minimum average delay, or equivalently the minimum average queue length, of message symbols randomly arriving to the transmitter queue of a point-to-point link which dynamically selects a (n, k) block code from a given collection. The system is modeled by a discrete time queue with an IID batch arrival process and batch service. We obtain a lower bound on the minimum average queue length, which is the optimal value for a linear program, using only the mean (λ) and variance (σ2) of the batch arrivals. For a finite collection of (n, k) codes the minimum achievable average queue length is shown to be Θ(1/ε) as ε ↓ 0 where ε is the difference between the maximum code rate and λ. We obtain a sufficient condition for code rate selection policies to achieve this optimal growth rate. A simple family of policies that use only one block code each as well as two other heuristic policies are shown to be weakly optimal in the sense of achieving the 1/ε growth rate. An appropriate selection from the family of policies that use only one block code each is also shown to achieve the optimal coefficient σ2/2 of the 1/ε growth rate. We compare the performance of the heuristic policies with the minimum achievable average queue length and the lower bound numerically. For a countable collection of (n, k) codes, the optimal average queue length is shown to be Ω(1/ε). We illustrate the selectivity among policies of the growth rate optimality criterion for both finite and countable collections of (n, k) block codes.

Queueing delay - error probability tradeoff for point-to-point channels with fixed length block codes

We study the tradeoff between the average error probability and the average queueing delay of messages which randomly arrive to the transmitter of a point-to-point discrete memoryless channel that uses variable rate fixed codeword length random coding. Bounds to the exponential decay rate of the average error probability with average queueing delay in the regime of large average delay are obtained. Upper and lower bounds to the optimal average delay for a given average error probability constraint are presented. We then formulate a constrained Markov decision problem for characterizing the rate of transmission as a function of queue size given an average error probability constraint. Using a Lagrange multiplier the constrained Markov decision problem is then converted to a problem of minimizing the average cost for a Markov decision problem. A simple heuristic policy is proposed which approximately achieves the optimal average cost.