Abstract Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under...

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch siz...

We consider the problem of dynamic admission control in a multi-class Markovian loss system receiving random batches, where each admitted class-i job demands an exponential service with rate μ, and brings a reward ri. We show that the optimal admission policy is a sequential threshold policy with monotone thresholds.

Abstract In this paper, we compute the probability generating functions (PGF’s) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be o...

We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping principle, we demonstrate the existence and uniqueness of a solution to the integral equation. Then we provide asymptotical analysis as well as tight bounds for the expected response time conditioned on the service time....

In this paper a study on the buffer overflow period in a finite-buffer queue is presented. A special attention is paid to the autocorrelation and batch arrivals, which are supposed to mimic the properties of real arrival processes. Using the batch Markovian arrival process, formulas for the duration of the first, subsequent and stationary overflow periods, as well as formulas for the distributi...

It is shown that a Markovian queue, with bulk arrivals and departures having any probability mass functions for their batch sizes, has geometrically distributed queue length at equilibrium (when this exists) provided there is an additional special bulk arrival stream, with particular rate and batch size distribution, when the server is idle. It is shown that the time-averaged input rate of the ...

Most research concerning batch-service queueing systems has focussed on some specific aspect of the buffer content. Further, the customer delay has only been examined in the case of single arrivals. In this paper, we examine three facets of a threshold-based batch-service system with batch arrivals and general service times. First, we compute a fundamental formula from which an entire gamut of ...