Task assignment with unknown duration
Journal of the ACM (JACM)
Delay moments for FIFO GI/GI/s queues
Queueing Systems: Theory and Applications
The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
Queueing Systems: Theory and Applications
Heavy Tails in Multi-Server Queue
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
On Large Delays in Multi-Server Queues with Heavy Tails
Mathematics of Operations Research
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Previously established necessary and sufficient conditions for finite stationary moments in stable FIFO GI/GI/s queues exist only for the first component of the workload vector, the delay, and the final component, which behaves as the total work in the system. In this paper, we derive moment results for all the components of the stationary workload vector in stable FIFO GI/GI/s queues. As in the case of stationary delay, the moment conditions for workload components incorporate the interaction between service-time distribution, traffic intensity and the number of servers in the queue.If we denote a generic service-time random variable by S, a generic interarrival time by T, and define the traffic intensity as 驴=ES/ET, then sufficient conditions for EW i W i is the ith smallest component of the ordered workload vector, depend crucially on the traffic intensity relative to i--specifically, on whether i驴驴驴驴 or i驴驴驴, where for any real x, 驴x驴 denotes the smallest integer greater than or equal to x. Explicitly, for i驴驴驴驴, $\mbox {E}W_{i}^{\alpha} , provided that $\mbox {E}S^{\beta_{1}(i)} , where β 1(i)=(s驴驴驴驴+驴)/(s驴驴驴驴), for 驴驴1. Furthermore, components with indices lower than 驴驴驴 all share the same finite moment conditions. This is not true for i驴驴驴; these components have individual finite moment conditions: $\mbox {E}W_{i}^{\alpha} provided that $\mbox {E}S^{\beta_{2}(i)} , where β 2(i)=(s驴i+驴)/(s驴i), for 驴驴1. Finally, for S in a large class of service distributions, these conditions are also necessary.