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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)

— As a natural multi-class generalization of the well-known (egalitarian) Processor Sharing (PS) service discipline, Discriminatory Processor Sharing (DPS) is of great interest in many application areas, including telecommunications. Under DPS, the mean response time conditional on the service requirement is only known in closed form when all classes have… (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)

Many mathematical models exist for describing the behavior of TCP/IP under an exogenous loss process that does not depend on the window size. The goal of this paper is to present a mathematical analysis of two asymmetric competing TCP connections where loss probabilities are directly related to their instantaneous window size, and occur when the sum of… (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… (More)

This paper considers the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting-or sojourn time distribution, demonstrating that different disciplines may lead to quite different tail behavior. The orientation of the paper is methodological: We outline three… (More)