Cost scrutiny of discrete-time priority queue with cluster arrival and Bernoulli feedback

Abstract

This work describes the economic feasibility of a single server discrete-time queueing model, (Geo/G/1) where interarrival times have a geometric distribution, and service times have a general distribution. This work is motivated by the case of discrete-time queueing models under priority scheme for solving many congestion issues of the telecommunication system wherein few calls are treated as prioritized calls and system manager may handle it properly. Herein a state-dependent arrival policy is used. It is assumed that the clients arrive in groups of varying sizes, and incorporates only one server queueing system with unlimited capacity. Under a discrete-time system with Markovian service practice, clients are serviced one at a time. If a client is dissatisfied with his service, he will most likely be directed back to the front of the queue. This concept is commonly referred to as Bernoulli feedback (BF) in queueing scenario. Just after every service, it is presumed that the server either starts to identify the next client to be serviced with some probability, or the server starts a solo vacation procedure with its complementary probability and this process is referred as Bernoulli vacation (BV). In addition, preferred and impatient clients are examined too. We investigate the Markov chain that underpins the queueing system in question, and its normalizing condition. The average number of consumers in the queue and the system are found using a generating function method. The numeral expositions are ascertained to delve the impact of different parameters on various performance metrics which can give information to system management in order to monitor the system's functioning condition and decrease congestion. We then used direct search method (DSM) and Particle Swarm Optimization (PSO) approaches to present a comparative study to assist system administrators or decision-makers by economically regulating the system. Furthermore, the results of the provided model are contrasted to those of a soft computing approach termed as ANFIS (Adaptive Neuro-Fuzzy Inference System).