For the M/M/1+M model at law-of-large-numbers scale, long-run reneging count per unit time does not depend on individual (i.e., customer) rate. This paradoxical statement has a simple proof. Less obvious is large deviations analogue of this fact, stated as follows: decay rate probability that atypically or small In paper, sample path principle for proved and function computed. Next, asymptotics...

ABSTRACT We analyze a single server queue with modified Bernoulli server vacations based on exhaustive service. Unlike other vacation policies, we assume that only at the completion of service of the last customer in the system, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The service times of the customers have been assum...

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoul...

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously sw...

We consider a closed queueing network, consisting of two FCFS single server queues in series: a queue with general service times and a queue with exponential service times. A fixed number N of customers cycles through this network. We determine the joint sojourn time distribution of a tagged customer in, first, the general queue and, then, the exponential queue. Subsequently, we indicate how th...

In this paper, we consider a single-server queue with stationary input, where each job joining the queue has an associated deadline. The deadline is a time constraint on job sojourn time and may be finite or infinite. If the job does not complete service before its deadline expires, it abandons the queue and the partial service it may have received up to that point is wasted. When the queue ope...

This short note discusses open problems and partial solutions related to Sheldon M Ross's second conjecture about the classical single server queue subject a randomly time-varying rate arrival rate.

Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomou...

This paper introduces the problem of optimally admitting a finite number of customers from an auxiliary buffer with a low holding cost into a single–server queue with a high holding cost without observing the status of the single-server queue. This paper formulates a static (off-line) optimization of the admission schedule for a finite number of customers, assuming that the single–server queue ...