Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services

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...

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server’s movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The se...

Light-Traffic Analysis for Queues with Spatially Distributed Arrivals

We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is “greedy”, in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served according to an arbitrary service time di...

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.