We consider a class of fluid queueing networks with multiple fluid classes and feedback allowed, which are fed by N heavy tailed ON/OFF sources. We study the asymptotic behavior when N → ∞ of these queueing systems in a heavy traffic regime (that is, when they are asymptotically critical). As performance processes we consider the workload W N (the amount of time needed for each server to comple...

We develop an approach to the analysis of average queueing delay in a tree network of discrete-time queues with constant senice time. The analysis of such systems is pertinent to packet-switehed data networks with fixed-length packets. Our solution is based on considering an equivalent network, in which at each node packets in transit are given priority over exogenous arrivals. The solution to ...

The expected wait in the Gi/G/1 queue is related to the mean and variance of the idle time. For arrival distributions which are 1FR or have mean residual life bounded by r-, simple bounds are obtained which A. give, for example, the expected number in queue to within at most one customer. By equating input with output, relations between random variables are used to obtain expressions foi the mo...

We consider a two-station tandem queueing system where customers arrive according to a Poisson process and must receive service at both stations before leaving the system. Neither queue is equipped with dedicated servers. Instead, we consider three scenarios for the fluctuations of workforce level. In the first, a decisionmaker can increase and decrease the capacity as is deemed appropriate; th...

A method is described for the efficient estimation of small overflow probabilities in nonMarkovian queueing network models. The method uses importance sampling with a state-dependent change of measure, which is determined adaptively using the cross-entropy method, thus avoiding the need for a detailed mathematical analysis. Experiments show that the use of rescheduling is needed in order to get...

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent r...

Performance evaluation plays a key role in manufacturing system design and productivity improvement. Characterizing performance objectively is the first step. Inspired by the underlying structure of tandem queues, we have derived an approximate model to characterize the system performance. The model decomposes system queue time and variability into bottleneck and non-bottleneck parts while capt...

This paper is written in honour to A. Hordijk. It establishes product form results for a generic and instructive multi-class tandem queue with blocking, to which A. Hordijk has directly and indirectly contributed. First, a sufficient and necessary product form characterization is provided. Next, three special cases are briefly presented. These illustrate the possibility of product forms despite...

This paper considers Gaussian flows multiplexed in a queueing network, where the underlying correlation structure is assumed to be short-range dependent. Whereas previous work mainly focused on the FIFO setting, this paper addresses overflow characteristics of more complex buffer architectures. We subsequently analyze the tandem queue, a priority system, and generalized processor sharing. In a ...

We present structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties. In addition to linear holding costs, we impose either lump sum switching costs or batch setup delays which are incurred at each instant the server processes a job in a queue diierent than the previous one. We use re...