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This paper studies the uid approximation, also known as the functional strong law-of-large-numbers, for a GI/G/1 queue under a processor-sharing service discipline. The uid (approximation) limit in general depends on the service time distribution, and the convergence is in general in the Skorohod J 1 topology. This is in contrast to the known result for the(More)
We consider two types of queues with workload-dependent arrival rate and service speed. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet. First, in the M/G/1 case, we compare the steady-state distribution of the workload (both at(More)
In this paper we generalize existing results for the steady state distribution of growth collapse processes. We begin with a stationary setup with some relatively general growth process and observe that under certain expected conditions point and time stationary versions of the processes exist as well as a limiting distribution for these processes which is(More)
We consider an M/G/1 queue with a removable server. When a customer arrives, the workload becomes known. The cost structure consists of switching costs, running costs, and holding costs per unit time which is a nonnegative nondecreasing right-continuous function of a current workload in the system. We prove an old conjecture that D-policies are optimal for(More)
Motivated by models of queues with server vacations, we consider a Lé vy process modified to have random jumps at arbitrary stopping times. The extra jumps can counteract a drift in the Lé vy process so that the overall Lé vy process with secondary jump input, can have a proper limiting distribution. For example, the workload process in an M/G/1 queue with(More)
In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that under some quite minimal conditions the local martingales are actually L 2 martingales which upon dividing by the time index converge to zero a.s. and in L 2. We apply these results to generalize known decomposition results for Lévy queues with(More)
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with an arrival rate that equals λ i when an external Markov process is in state i. The service times have a general distribution that depends on the state of the background process upon arrival. We start by setting up explicit formulas for the mean and(More)