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Motivated by queues with service interruptions, we consider an infinite-capacity storage model with a two-state random environment. The environment alternates between ‘‘up’’ and ‘‘down’’ states. In the down state, the content increases according to one stochastic process; in the up state, the content decreases according to another stochastic process. We(More)
We consider a storage model which can be on or off. When on, the content increases at some state-dependent rate and the system can switch to the off state at a state-dependent rate as well. When off, the content decreases at some statedependent rate (unless it is at zero) and the system can switch to the on position at a state-dependent rate. This process(More)
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)
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 martingales which upon dividing by the time index converge to zero a.s. and in L. We apply these results to generalize known decomposition results for Lévy queues with(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)
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)
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)