We study a discrete-time deterministic server queue with infinite buffer and with packet arrivals that depend on a multidimensional Markov process. Using the generating functions approach we give a means for obtaining the boundary conditions vector for the case where the value zero is a multiple eigenvalue of the problem. We also derive recursive form expressions for the direct determination of...

In this note we consider M/D/1/N queue with renovation and derive analytic expressions for the following performance characteristics: stationary loss rate, moments of the number in the system. Moments of consecutive losses, waiting/sojourn time (as introduced in [1]) are out of scope. The motivation for studying these characteristics is in the comparison of renovation with known active queue me...

We consider queuing systems with coupled processors, where the service rate at each queue varies depending on the set of queues in the system with non-zero queue lengths. In general, such queuing systems are very difficult to analyze and steady state queue length distributions are known only for two-queue systems. The coupled-processors model arises naturally in the study of several systems whe...

We use Palm measures, along with a simple approximation technique to derive new explicit expressions for all of the transient moments of the workload process of an M/G/1 queue. These expressions can also be used to derive a closed-form expression for the nth moment of the stationary workload, which solves the well-known Takács recursion that generates the waiting time moments of an M/G/1 queue ...

This paper reports a study on a single server queue with bulk arrival and bulk service patterns wherein the incoming traffic depends on the state of the server which may be in operating or breakdown state. The repair of the breakdown server is performed in two phases. The operating duration of server, repair duration of both phases of repairing as well as job's inter-arrival times and service t...

In this paper we consider the MMAP/PH/1 priority queue, both the case of preemptive resume and the case of non-preemptive service. The main idea of the presented analysis procedure is that the sojourn time of the low priority jobs in the preemptive case (and the waiting time distribution in the nonpreemptive case) can be represented by the duration of the busy period of a special Markovian flui...

We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Sze...

The class of Gaussian processes is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space, or time and space. The popularity of such processes stems primarily from two essential properties. First, a Gaussian process is completely determined by its mean and covariance functions. This property facilitates model fitting as only the fir...