A Finite Capacity Single Server Queue with Flexible Service Rate

Abstract

The model analyzed in this paper has the assumption: arrival process is poisson       with state-dependent parameters, service time distribution is negative exponential with state-dependent rate, if there are n customers in the system then the arrival rate λ_n , Service rate μ_n, when an arrival finds the server free, the customer immediately enters the service station, otherwise the customer enters into a queue of size N(N>0), in the waiting line the waiting customer applies First come First service discipline and during the service period of the customer, if the customer satisfied with the service at any instant of the service period, the customer leaves the system with probability δ or continue with probability 1- δ, now the service rate becomes 1/δ (service rate) (0< δ≤1). This model defined using the infinitesimal generator matrix and for the analysis, the group generalised inverse of the infinitesimal generator is used. Using the group generalised inverses, the steady-state probabilities are obtained analytically. Performance measures based on the same are derived. In addition, some numerical illustrations are provided.