We consider a storage model that can be either interpreted as a certain queueing model with dependence between a service request and the subsequent interarrival time, or as a fluid production/inventory model with a two-state random environment. We establish a direct link between the workload distributions· of the queueing model and the production/inventory model, and we present a detailed analy...

Abstract: The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global maxima is proved in the phases of a queueing system studied for an important probability characteristic of the system (total waiting time of a customer and waiting time of a custom...

We study the single server queueing system with two types of Abstract failure to servicechannels including the preemptive priority to the repair of major failure. The units arrive at thesystem in a poisson fashion and are served exponenitally. The steady - state probabilities ofvarious states by using generating function have been obtained.

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...