Abstract
The present paper deals with an M^{X}/M/c Bernoulli feedback queueing system with variant multiple working vacations and impatience timers which depend on the states of the servers. Whenever a customer arrives at the system, he activates an random impatience timer. If his service has not been completed before his impatience timer expires, the customer may abandon the system. Using certain customer retention mechanism, the impatient customer can be retained in the system. After getting incomplete or unsatisfactory service, with some probability, each customer may comeback to the system as a Bernoulli feedback. Using the probability generating functions (PGFs), we derive the steady-state solution of the model. Then, we obtain useful performance measures. Moreover, we carry out an economic analysis. Finally, numerical study is performed to explore the effects of the model parameters on the behavior of the system.
Highlights
Vacation queueing models with impatient customers are very helpful in providing basic framework for efficient design and study of diverse practical situations including telephone switchboard, inventory problems with perishable goods, computer and communication network, data/voice transmission, manufacturing system, etc.In recent past, vacation queueing models have been widely studied
We carry out the analysis of an M X /M/c Bernoulli feedback queueing model with variant of multiple working vacations, reneging which depend on the states of the servers and retention of reneged customers
To the best of our knowledge, modeling of multi-server queueing system with Bernoulli feedback, variant of working vacations, impatience timers which depend on the states of the servers, and retention of reneged customers has not been attempted in the literature
Summary
Vacation queueing models with impatient customers are very helpful in providing basic framework for efficient design and study of diverse practical situations including telephone switchboard, inventory problems with perishable goods, computer and communication network, data/voice transmission, manufacturing system, etc. In Bouchentouf and Yahiaoui [2], a study on queueing system with Bernoulli feedback, reneging and retention of reneged customers, multiple working vacations, and Bernoulli schedule vacation interruption has been done. We carry out the analysis of an M X /M/c Bernoulli feedback queueing model with variant of multiple working vacations, reneging which depend on the states of the servers and retention of reneged customers. To the best of our knowledge, modeling of multi-server queueing system with Bernoulli feedback, variant of working vacations, impatience timers which depend on the states of the servers, and retention of reneged customers has not been attempted in the literature.
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