Petar Momcilovic

Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue

We investigate the distribution of the waiting timeV in a stable M/G/1 processor-sharing queue with traffic intensityp x] = P[ B > (1 -p) x](1 +o(1)) as x ? 8. Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail thane-vx.

On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers

The interface between an emergency department and internal wards is often a hospitals bottleneck. Motivated by this interaction in an anonymous hospital, we analyze queueing systems with heterogeneous server pools, where the pools represent the wards, and the servers are beds. Our queueing system, with a single centralized queue and several server pools, forms an inverted-V model. We introduce the randomized most-idle (RMI) routing policy and analyze it in the quality-and efficiency-driven regime, which is natural in our setting. The RMI policy results in the same server fairness (measured by idleness ratios) as the longest-idle-server-first (LISF) policy, which is commonly used in call centers and considered fair. However, the RMI policy utilizes only the information on the number of idle servers in different pools, whereas the LISF policy requires information that is unavailable in hospitals on a real-time basis. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Large Deviations of Square Root Insensitive Random Sums

We provide a large deviation result for a random sum S Nxn=0 X n , whereN xis a renewal counting process and { X n } n=0are i.i.d. random variables, independent ofN x , with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier thane -vxand have zero relative decrease in intervals of length v x, hence square root insensitive. Using this result we derive the asymptotic characterization of the busy period distribution in the stable GI/G/1 queue with square root insensitive service times; this characterization further implies that the tail behavior of the busy period exhibits a functional change for distributions that are lighter thane -vx .

Steady-state analysis of a multiserver queue in the Halfin-Whitt regime

We consider a multiserver queue in the Halfin-Whitt regime: as the number of servers n grows without a bound, the utilization approaches 1 from below at the rate Assuming that the service time distribution is lattice valued with a finite support, we characterize the limiting scaled stationary queue length distribution in terms of the stationary distribution of an explicitly constructed Markov chain. Furthermore, we obtain an explicit expression for the critical exponent for the moment generating function of a limiting stationary queue length. This exponent has a compact representation in terms of three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly, it matches an analogous exponent corresponding to a single-server queue in the conventional heavy-traffic regime.

Flood search under the California Split rule

We consider flood search on a line and show that no algorithm can achieve an average-case competitive ratio of less than 4 when compared to the optimal off-line algorithm. We also demonstrate that the optimal scanning sequences are described by simple recursive relationships that yield surprisingly complex behavior related to Hamiltonian chaos.

The Dyadic Stream Merging Algorithm

We study the stream merging problem for media-on-demand servers. Clients requesting media from the server arrive by a Poisson process, and delivery to the clients starts immediately. Clients are prepared to receive up to two streams at any time, one or both being fed into a buffer cache. We present an on-line algorithm, the dyadic stream merging algorithm, whose recursive structure allows us to derive a tight asymptotic bound on stream merging performance. In particular, let ? be the Poisson request arrival rate, and let L be the fixed media length. Then the long-time ratio of the expected total stream length under the dyadic algorithm to that under an algorithm with no merging is asymptotically equal to 3log(?L)2?L. Furthermore, we establish the near-optimality of the dyadic algorithm by comparisons with experimental results obtained for an optimal algorithm constructed as a dynamic program. The dyadic algorithm and the best on-line algorithm of those recently proposed differ by less than a percent in their comparison with an off-line optimal algorithm. Finally, the worst-case performance of our algorithm is shown to be no worse than that of earlier algorithms. Thus, the dyadic algorithm appears to be the first near optimal algorithm that admits a rigorous average-case analysis.

Scalability of wireless networks

This paper investigates the existence of scalable protocols that can achieve the capacity limit of c/√N per source-destination pair in a large wireless network of N nodes when the buffer space of each node does not grow with the size of the network N. It is shown that there is no end-to-end protocol capable of carrying out the limiting throughput of c/√N with nodes that have constant buffer space. In other words, this limit is achievable only with devices whose buffers grow with the size of the network. On the other hand, the paper establishes that there exists a protocol which realizes a slightly smaller throughput of c/√N log N when devices have constant buffer space. Furthermore, it is shown that the required buffer space can be very small, capable of storing just a few packets. This is particularly important for wireless sensor networks where devices have limited resources. Finally, from a mathematical perspective, the paper furthers our understanding of the difficult problem of analyzing large queueing networks with finite buffers for which, in general, no explicit solutions are available.

Resource sharing with subexponential distributions

We investigate the distribution of the waiting time V in an M/G/1 processor sharing queue with traffic intensity /spl rho/ < 1. This queue represents a baseline model for evaluating efficient and fair network resource sharing algorithms, e.g. TCP flow control. When the distribution of job size B belongs to a class of subexponential distributions with tails heavier than e/sup -/spl radic/x/, it is shown that as x/spl rarr//spl infin/ P[V > x] = P[B > (1 - /spl rho/)x](1 + o(1)) Furthermore, we demonstrate that the preceding relationship does not hold if the job distribution has a lighter tail than e/sup -/spl radic/x/. This result provides a new tool for analyzing network congestion points with moderately heavy-tailed characteristics, e.g. log normal distributions, that have been recently empirically discovered in Web traffic. The accuracy of our approximation is confirmed with simulation experiments.

Reduced Load Equivalence under Subexponentiality

AbstractThe stationary workload WA+Bφ of a queue with capacity φ loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and