In this note we develop a framework for computing upper and lower bounds of an exponential form for a class of stochastic recursive equations with uniformly recurrent Markov modulated inputs. These bounds generalize Kingman's bounds for queues with renewal inputs. Copyright Springer-Verlag...

Understanding the behavior of an idle time of a limited resource is the key to increase productivity in service operations. When the system consists of nonexponential properties of time distributions it becomes difficult to provide results for the general case. We derive the MacLaurin series for...

We consider the processor sharing M/M/1-PS queue which also models balking. A customer that arrives and sees n others in the system “balks” (i.e., decides not to enter) with probability 1−b n . If b n is inversely proportional to n + 1, we obtain explicit expressions for a tagged...

This short communication considers the workload process of a queue operating in slotted time, focusing on the (multivariate) distribution of the workloads at different points in time. In a many-sources framework exact asymptotics are determined, relying on large-deviations results for the sample...

We deal with a cost-allocation problem arising from sharing a medical service in the presence of queues. We use a standard queuing theory model in a context of several medical procedures, a certain demand for treatment and a maximum average waiting-time guaranteed by the government. We show that...

The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing system where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity...

Structural properties of generalised semi-Markov processes (GSMP) have been successfully studied in the literature. Examples are the celebrated commuting condition (CC), which is the key condition for unbiasedness of the infinitesimal perturbation analysis (IPA) gradient estimator, or the...