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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 study an M/G/1 queue with impatience and an adap-tive arrival process. The rate of the arrival process changes according to whether an incoming customer is impatient or not. We obtain the Laplace-Stieltjes Transform of the joint stationary workload and arrival rate process. This queueing model also captures the interaction between(More)
In this paper we generalize existing results for the steady state distribution of growth collapse processes with independent exponential inter-collapse times to the case where they have a general distribution on the positive real line having a finite mean. In order to compute the moments of the stationary distribution, no further assumptions are needed.(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)
We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content(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)
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)