Multi–server loss queueing system with random volume customers, non–identical servers and a limited sectorized memory buffer

Abstract

In the present paper, the model of multi–server queueing system with random volume customers, non–identical (heterogeneous) servers and a sectorized memory buffer has been investigated. In such system, the arriving customers deliver some portions of information of a different type which means that they are additionally characterized by some random volume vector. This multidimensional information is stored in some specific sectors of a limited memory buffer until customer ends his service. In analyzed model, the arrival flow is assumed to be Poissonian, customers’ service times are independent of their volume vectors and exponentially distributed but the service parameters may be different for every server. Obtained results include general formulae for the steady–state number of customers distribution and loss probability. Special cases analysis and some numerical computations are attached as well.

Keywords

• multi–server queueing system with heterogeneous servers
• queueing systems with random volume customers
• sectorized memory buffer
• loss probability
• stieltjes convolution