A two-priority single server retrial queue with additional items

Abstract

In this paper, we study a priority queueing-inventory problem with two types of customers. Arrival of customers follows Marked Markovian arrival process and service times have phase-type distribution with parameters depending on the type of customer in service. For service of each type of customer, a certain number of additional items are needed. High priority customers do not have waiting space and so leave the system when on their arrival a priority 1 customer is in service or the number of available additional items is less than the required threshold. Preemptive priority is assumed. Type 2 customers, encountering a busy server or idle with the number of available additional items less than a threshold, go to an orbit of infinite capacity to retry for service. The customers in orbit are non-persistent: if on retrial the server is found to be busy/idle with the number of additional items less than the threshold, this customer abandons the system with certain probability. Such a system represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems. The probability distribution of the system states is computed, using which several of the characteristics are derived. A detailed numerical study of the system, including the analysis of the influence of the threshold, is performed.

Stochastic decomposition in retrial queueing-inventory system

“…Stationary distributions of the system states and the waiting time are computed. Dhanya et al [9] extended findings in Baek et al [2] to retrial of low priority customers.…”

“…In Figure 2, we notice that as service rate µ is varied, keeping (s, S, λ, γ, θ) = (20, 45, 8,2,9), the probability of server being idle increases with increase in service rate. This could be attributed to the fact that, server becomes idle with faster rate of service.…”

Modified Erlang Loss System for Cognitive Wireless Networks

“…Salameh et al [10,11] consider models with a limited number of sensing secondary users. Other queueing models of cognitive radio networks could be found in [10,[12][13][14][15][16][17]. In [10,13,16,18], the service time distributions of primary and secondary customers are either restricted to Markovian distributions (exponential or phase-type distributions) and/or the assumption that the number of active secondary users are finite.…”

Modified Erlang loss system for cognitive wireless networks

“…Salameh et al [9,10] consider models with limited number of sensing secondary users. Other queueing models of cognitive radio networks could be found in [11][12][13][14][15][16][17]. In [11][12][13]18], the service time distributions of primary and secondary customers are either restricted to Markovian distributions (exponential or phase-type distributions) and/or the assumption that the number of active secondary users are finite.…”

“…In [11][12][13]18], the service time distributions of primary and secondary customers are either restricted to Markovian distributions (exponential or phase-type distributions) and/or the assumption that the number of active secondary users are finite. In [14,15,17,[19][20][21][22][23], models with single channel are investigated.…”