Transient analysis of impatient customers in an M/M/1 disasters queue in random environment

Purpose This paper aims to consider a single server queue with system disasters and impatience behavior are evident in our daily life. For this purpose, authors require to know the general behavior of these systems. Transient analysis shows for us how the system will operate up to some time instant t. Design/methodology/approach In this paper, authors consider a single server queue with system disaster and impatient behavior of customers in a multi-phase random environment, in which the system transits to a repair state after each system disaster. When the system is in a failure phase or going through a repair phase, the new arrivals would be impatient. In case the system is not repaired before the customer’s time expires, the customer would leave the queue and never return. Moreover, after repair, the system becomes ready for service in an operative phase with probability $q_{i} \ge 0.$. Using generating functions along with continued fractions and some properties of the confluent hypergeometric function, authors obtained on their own results. Findings Explicit expressions have been obtained for the time-dependent probabilities of the underlying queuing model. Also, time-dependent mean and variance of customers in the system are deduced. Research limitations/implications The system authors are dealing with is somewhat complicated, there are some performance measures that cannot be achieved, but some of them have been obtained, such as the expectation and variance of the number of customers in the system. Practical implications Based on the obtained results, some numerical examples are some numerical examples are presented to illustrate the effect of various parameters on the behavior of the proposed system. Social implications Authors’ studied transient analysis of a single server queue with system disaster and impatient customer system is suitable for behavior interpretation of many systems in our lives, such as telecommunication networks, inventory systems and impatient telephone switchboard customers, manufacturing system and service system. Originality/value To the best of the author’s/authors’ knowledge and according to the literature survey, in a multi-phase random environment, no previous published article is presented for transient analysis of a single server queue with system disaster and impatient customer behavior in a random environment.

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

Asymptotic Results for Buffer Systems under Heavy Load

This paper considers a dam (or storage) model of the GI/G/I type with a finite capacity K. An arriving input being larger than the unfilled capacity of the dam causes an overflow where the excess amount is lost. Important performance measures for this system are the overflow probability and the long-run fraction of input that is lost. We give asymptotic expansions for these measures for large K both for the case of a load factor less than 1 and for the case of a load factor larger than 1. Also, related results are obtained for the impatient customer model of the M/G/l type.