Abstract
In this research work we are concerned with single unit server queue queue with Markov Modulated process in Poisson fashion and the service time follow exponential distribution. The system is framed as a state dependent with the arrival process as Markov Modulated input and service is rendered by a single server with variation in service rate based on the intensity of service state of the system. The rate matrix that is essential to compute the stationary probability vector is obtained and various performance measures are computed using matrix method.
Highlights
Queuing systems is a mathematical phenomenon that has wide range of applications in computer systems and communication networks
The queuing model whose work load based on dependent service rate was investigated by [3] and obtained the combined probability distribution 0f queue length at individual station depending on change in service rate
Some of the well-known counting processes are Poisson processes (PP) which is a classic in stochastic study, Markov Modulated Poisson processes (MMPP) which behaves like switch over to two different arrivals, renewal processes that repeats over a period of time etc
Summary
Queuing systems is a mathematical phenomenon that has wide range of applications in computer systems and communication networks. The customer(packets) arrive to the system and wait in the buffer to be serviced, if the server fails to provide service immediately where there are many packets to be transferred that may suffer a long delay which load to poor performance This situation can be represented by performance of queuing system with waiting length dependent on increased arrival or poor services. The work carried out here is to study the state dependent quasi birth death process with MMPP inputs and the nature of problems of such special process are sometimes difficult to represent in structure. Some researchers [1, 5] suggested and proposed the revised algorithm of [8] according the model of state dependent quasi birth death process which made comfortable in matrix structure applying some analytic concepts on it. The description of this work as queuing model is presented
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