M/G/n/(0, V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space

Abstract

In the present paper, we investigate a multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.

Keywords

• multi-server queueing systems
• queueing systems with non-homogeneous customers
• queueing systems with heterogeneous servers
• loss probability
• stieltjes convolution