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In this note we explore a useful equivalence relation for the delay distribution in the G/M/1 queue under two different service disciplines: (i) PS (Processor Sharing); and (ii) ROS (Random Order of Service). We provide a direct probabilistic argument to show that the sojourn time under PS is equal (in distribution) to the waiting time under ROS of a(More)
—In this paper we obtain the scaling law for the mean broadcast time of a file in a P2P network with an initial population of N nodes. In the model, at Poisson rate λ a node initiates a contact with another node chosen uniformly at random. This contact is said to be successful if the contacted node possesses the file, in which case the initiator downloads(More)
Over the past few decades, the Processor-Sharing (PS) discipline has attracted a great deal of attention in the queueing literature. While the PS paradigm emerged in the sixties as an idealization of round-robin scheduling in time-shared computer systems, it has recently captured renewed interest as a useful concept for modeling the flow-level performance(More)
For the GGGG1 queue with First-Come First-Served, it is well known that the tail of the sojourn time distribution is heavier than the tail of the service requirement distribution when the latter has a regularly varying tail. In contrast, for the MMGG1 queue with Processor Sharing, Zwart and Boxma 26 showed that under the same assumptions on the service(More)
We consider a multi-class queueing system operating under the discriminatory processor-sharing (DPS) discipline. The DPS discipline provides a natural approach for modeling the flow-level performance of differentiated bandwidth-sharing mechanisms. Motivated by the extreme diversity in flow sizes observed in the Internet, we examine the system performance in(More)
We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index −ν, it is shown that the waiting time distribution is also(More)
Motivated by scheduling in cellular wireless networks and resource allocation in computer systems, we study a service facility with two classes of users having heterogeneous service requirement distributions. The aggregate service capacity is assumed to be largest when both classes are served in parallel, but giving preferential treatment to one of the(More)
We study the sojourn time of customers in an M/M/1 queue with processor sharing service discipline and service interruptions. The lengths of the service interruptions have a general distribution, whereas the periods of service availability are assumed to have an exponential distribution. A branching process approach is shown to lead to a decomposition of(More)