Geom/G1, G2/1/1 REPAIRABLE ERLANG LOSS SYSTEM WITH CATASTROPHE AND SECOND OPTIONAL SERVICE

This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.