Systems whose arrival or service rates fluctuate over time are very common, but are still not well understood analytically. Stationary formulas are poor predictors of systems with fluctuating load. When the arrival and service processes fluctuate in a Markovian manner, computational methods, such as Matrix-analytic and spectral analysis have been instrumental in the numerical evaluation of quan...

This paper considers a heterogeneous M / G/2 queue. The service times at server 1 are exponentially distributed, and at server 2 they have a general distribution BO. We present an exact analysis of the queue length and waiting time distribution in case B(·) has a rational Laplace-Stieltjes transform. When B(·) is regularly varying at infinity of index -lI, we determine the tail behaviour of the...

ALNOWIBET, KHALID ABDULAZIZ Nonstationary Erlang Loss Queues and Networks. (Under the direction of Dr. Harry Perros) The nonstationary Erlang loss model is a queueing system consisting of a finite number of servers and no waiting room with a nonstationary arrival process or a time-dependent service rate. The Erlang loss model is commonly used to model and evaluate many communication systems. Of...

We prove a functional central limit theorem for Markov additive arrival processes (MAAPs) where the modulating Markov process has the transition rate matrix scaled up by n (α > 0) and the mean and variance of the arrival process are scaled up by n. It is applied to an infinite-server queue and a fork-join network with a non-exchangeable synchronization constraint, where in both systems both the...

Architectures parall eles, Bases de donn ees, R eseaux et Syst emes distribu es Abstract Consider a polling system with K 1 queues and a single server that visits the queues in a cyclic order. The polling discipline in each queue is of general gated-type or exhaustive-type. We assume that in each queue the arrival times form a Poisson process, and that the service times, the walking times as we...

This essay, based on my 2012 MSOM Fellow Lecture, discusses an idea that has been useful for developing effective methods to set staffing levels in service systems: offered load analysis. The main idea is to tackle a hard problem by first seeking an insightful simplification. For capacity planning to meet uncertain exogenous demand, offered load analysis looks at the amount of capacity that wou...

This paper studies the M/M/s+M queue, i.e., the M/M/s queue with customer abandonment, also called the Erlang-A model, having independent and identically distributed customer abandon times with an exponential distribution (the +M), focusing on the case in which the arrival rate and the number of servers are large. The goal is to better understand the sensitivity of performance to changes in the...

The main theme of this paper is to find the Distributed Data Transaction of an Apache web server using bulk service rule. We obtain the parameter of service rate, Arrival rate, Expected waiting time and Expected Busy period. The inter arrival and inter service of HTTP request is assumed to Poisson Distribution Process (PDP) and these events are considered in the server for process sharing. The ...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity pre...