ALGORITHMIC METHODS FOR PH/PH/1 QUEUES WITH BATCH ARRIVALS OR SERVICES

Algorithmic Methods for Ph / Ph / 1 Queues with Batch Arrivals or Services

We discuss algorithms for the computation of the steady state features of PH/PH/l queues with bounded batch arrivals or batch services. Many characteristic quantities such as the mean and variance of queue length in continuous time, the mean waiting time, the waiting probability, etc. are obtained in computationaJIy tractable forms. We also show various numerical values.

Numerical analysis of queues with batch arrivals

Infinite-server Queues with Batch Arrivals and Dependent Service Times

Motivated by large-scale service systems, we consider an infinite-server queue with batch arrivals, where the service times are dependent within each batch. We allow the arrival rate of batches to be time-varying as well as constant. As regularity conditions, we require that the batch sizes be i.i.d. and independent of the arrival process of batches, and we require that the service times within...

Poisson and Gaussian Approximations for Multi-Server Queues with Batch Arrivals and Batch Abandonment

In this paper, we consider nonstationary multi-server queues and multiserver loss queues with batch arrivals and where we allow customer abandonment to also occur as a Markovian batch process. To estimate the performance of the system, we develop two new approximations that take advantage of the functional Kolmogorov forward equations. The first approximation we develop uses the Poisson distrib...

Synchronized queues with deterministic arrivals

We consider m independent exponential servers in parallel, driven by the same deterministic input. This is a modification of the Flatto-Hahn-Wright model which turns out to be easily tractable. We focus on the time-stationary distribution of the number of customers which is obtained using the Palm inversion formula.