Sergey Foss

On Large Delays in Multi-Server Queues with Heavy Tails

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s-k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

Large-scale join-idle-queue system with general service times

A parallel server system with

Stability of a Markov-modulated Markov chain, with application to a wireless network governed by two protocols

n

Heavy-Tailed and Long-Tailed Distributions

identical servers is considered. The service time distribution has a finite mean

Spatial Loss Systems: Exact Simulation and Rare Event Behavior

1/\mu

Stochastic Stability of Monotone Economies in Regenerative Environments

, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where

Random multiple access system with a common energy supply

n\to\infty

Limiting Properties of Random Graph Models with Vertex and Edge Weights

and the customer input flow rate is

Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions

\lambda n

Two-dimensional ruin probability for subexponential claim size

. Under the condition