Sensitivity analysis is done on the assumption of geometric batch arrivals used by several authors in the study of tradeoffs between real-time and non-real-time trafJic in a statistical multiplexer. This work finds the geometric batch arrival assumption conservative compared with correlated MMPP’s. The Poisson arrival assumption is much more optimistic that the geometric batch arrival assumption.

a two server queueing system with single and batch service is considered in this paper. the arrival process is assumed to be poisson and the service rate follows an exponential distribution. server-i serves the customers in both single and batch service, while server-ii serves the customers in batch service only. the laplace transform of the transient and steady state behavior of the model is c...

This article describes the batch Markovian arrival process (BMAP), a point process that is characterized by Markov-modulated batch arrivals of random size. The BMAP is a generalization of many well-known processes including the Markovian arrival process (MAP), the Poisson process, and the Markov-modulated Poisson process. It provides a common framework for modeling arrival processes in a variet...

In this paper an emergency service vehicle (ESV) location problem has been considered in which it is assumed that each emergency call may require more than one ESV. In ESV location problem two factors should be known; the location of stations and the number of ESVs at each station. Hence, a nonlinear mixed integer programming model is presented in order to maximize the total response rate to th...

A single-server queueing model with infinite buffer and batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of an accepted batch arrive one by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival pro...

A multiserver queueing model that does not have a buffer but has batch arrival of customers is considered. In contrast to the standard batch arrival, in which the entire batch arrives at the system during a single epoch, we assume that the customers of a batch flow arrive individually in exponentially distributed times. The service time is exponentially distributed. Flows arrive according to a ...

This work constructs the membership functions of the system characteristics of a batch-arrival queuing system with multiple servers, in which the batch-arrival rate and customer service rate are all fuzzy numbers. The  -cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, ...

This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival,...

This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted are served by single server. The service is assumed to be dependent on batch-size follows general bulk rule. inter-arrival times of correlated they represented through batch Markovian arrival process (BMAP). Computation procedure queue-length distributions at post-batch-service completion, an...