Mokhtar Kadi

Bio: Mokhtar Kadi is an academic researcher. The author has contributed to research in topics: Queue. The author has an hindex of 1, co-authored 2 publications receiving 2 citations.

Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers

Abstract: This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.

Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

Abstract: This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using the probability generating function (PGF) technique, we obtain the steady-state solution of the system. Besides, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using a quadratic fit search method (QFSM). Finally, numerical examples are provided to visualise the analytical results.

Performance measures of variant working vacations on batch arrival queue with reneging

Abstract: T his paper analyzes a batch arrival infinite-buffer single server queueing system with variant working vacations wherein customers arrive according to a Poisson process As soon as the system becomes empty, the server takes working vacation The service times during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed and are mutually independent During working vacations the customer may renege and the reneging time follows exponential distribution We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size when the server is in different states In addition, we obtain some other performance measures and discuss their monotonicity A cost model is formulated to determine the optimal service rate during working vacation and regular busy period

Performance Analysis of a Markovian Queue with Impatient Customers and Working Vacation

Abstract: In this paper, we consider the impatient customers in M/M/1 queueing model under variant working vacation policy. The customer’s impatience is due to its arrival during a working vacation period, where the service rate of the customer is lower than a normal busy period. If the system is non-empty when the server returns from the working vacation, the server resumes the normal service period. Otherwise, the server will take successive working vacations till it reaches the maximum number of K working vacations and then the server remains idle until the next arrival. Closed-form probabilities are obtained by using the identities involving beta functions and degenerate hypergeometric functions, and the performance measures of the system are derived using generating functions. The stochastic decomposition structures of the mean queue length and mean waiting time are verified. The effects of the system parameters on some performance measures had been numerically illustrated.

Analysis of a batch arrival multi-server queueing system with waiting servers, synchronous working vacations and impatient customers

Abstract: Abstract This paper is concerned with the analysis of an infinite-capacity batch arrival multi-server queueing system with Bernoulli feedback, synchronous multiple and single working vacation policies, waiting servers, reneging and retention of reneged customers. The steady-state solution of the queueing system is obtained by using probability generating function (PGF). In addition, important performance measures of the queueing system are derived. Then, a cost model is formulated in order to carry out the parameter optimization using genetic algorithm (GA). Finally, numerical study is presented in which various system performance measures are evaluated based on supposed numerical values given to the system parameters.

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Abstract: This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.