Discrete-Time Analysis of Communication Networks with Second Optional Service and Negative User Arrivals

Unreliable G-queues with the option of an additional service are appropriate mathematical models for communication networks, and hence, their performance evaluation is important for theory and applications. The present work investigates a Geo/Geo/1 G-queue with second optional service (SOS) and unreliable server. We assume that in addition to normal (positive) arriving customers, negative customers also arrive in the system. A customer in service is taken away upon a negative customer arrival, which also causes the failure of server. We consider that all arriving customers are provided with the essential service, which is known as first essential service (FES) and some customer’s desire for an optional service after essential service with a certain probability, which is known as second optional service (SOS). The steady-state probabilities and expected number of customers in the system, throughput, and delay are derived using the matrix geometric method. Further, numerical simulations are computed to illustrate the joint influence of an optional service and the unreliable server on the performance of the communication networks.