8 papers found.

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We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by a shot-noise process. A shot-noise rate emerges naturally in cases where the arrival rate tends to exhibit sudden increases (or shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential...

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of Lévy input, covering compound Poisson, \(\alpha \)-stable Lévy motion (with \(1<\alpha <2\)), and Brownian motion. In our analysis, we separately deal with Lévy input processes with increments that have finite and infinite variance. A distinguishing...

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The...

We study an M/G/1 processor sharing queue with multiple vacations. The server only takes a vacation when the system has become empty. If he finds the system still empty upon return, he takes another vacation, and so on. Successive vacations are identically distributed, with a general distribution. When the service requirements are exponentially distributed we determine the...

In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let \(\{Y^{(a)}_{n}:n\ge1\}\) be a sequence of independent and identically distributed random variables and \(\{X^{(a)}_{t}:t\ge0\}\) be a Lévy process such that \(X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)}\), \(\mathbb{E}X_{1}^{(a)}<0\) and...

We consider an extension of the standard G/G/1 queue, described by the equation \(W\stackrel{ \mathcal {D}}{=}\max\mathrm{max}\,\{0,B-A+YW\}\) , where ℙ[Y=1]=p and ℙ[Y=−1]=1−p. For p=1 this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for p=0 it describes the waiting time of the server in an alternating service model. For all...

In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study the joint queue length distribution at polling epochs and at the server’s departure epochs. We also study the marginal queue...