We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches, where each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of “preferred class” for systems receiving mixed and one-class batches separately, and derive sufficient conditions for ea...

This paper considers the problem of minimizing make-span and maximum tardiness simultaneously for scheduling jobs under non-identical job sizes, dynamic job arrivals, incompatible job families,and sequence-dependentfamily setup time on the single batch- processor, where split size of jobs is allowed between batches. At first, a new Mixed Integer Linear Programming (MILP) model is proposed for t...

— We consider in this paper the steady state behaviour of a Queueing System with queue length dependent additional server facility wherein arrivais occur in batches of variable size. Whenever the queue length in front of the first server reaches a certain lenght, the system adds another server. Steady state probabilities and expected queue lengths in Single Server System and Additional Server S...

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...

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...

This paper considers an infinite-server queue with multiple batch Markovian arrival streams. The service time distribution of customers may be different for different arrival streams, and simultaneous batch arrivals from more than one stream are allowed. For this queue, we first derive a system of ordinary differential equations for the time-dependent matrix joint generating function of the num...

We study a simple network with two parallel batch service queues, where service at a queue commences when the batch is full and each queue is served by infinitely many servers. A stream of general arrivals observe the current state of the system on arrival and choose which queue to join to minimize their own expected transit time. We show that for each set of parameter values there exists a uni...

In this paper we consider a slotted queueing model with nite buuers and correlated input. Arrivals are generated by diierent sources and ooered in batches at the end of each slot. The batch sizes depend on the states of the sources which change their states according to Markov schemes. In case that the buuer reaches its limits, the excess of the buuer is lost. At the end of a slot a random batc...

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...