In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following Poisson process and server operates under (a,b)-bulk service rule. The system has finite-buffer capacity ‘N’ excluding batch service. service-time of batches follows general distribution, is independent arrival process. We first develop an alterna...

The purpose of this research in the queueing theory is the theorem about the law of the iterated logarithm in multiphase queueing systems and its application to the mathematical model of the message switching system. First the law of the iterated logarithm is proved for the cumulative idle time of a customer. Finally we present an application of the proved theorem for the model of the message s...

We consider a two-priority queueing system which represents an ATM node serving both variable bit rate (VBR) and unspeciied bit rate (UBR) traac. We determine the (transmission or link) capacity necessary for each traac type to guarantee prespeciied quality of service (QoS) requirements. This is done by means of a steady state performance analysis of the tail distribution of the buuer occupanci...

We consider priority fluid queueing systems where high priority class has strict priority access to service. Sample path analysis tools, such as Poisson Counter Driven Stochastic Differential Equation, are employed to study system queueing behavior in steady state. We are able to obtain various analytical results for different fluid traffic models and system configurations. Those results can be...