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A finite state Markovian queue to let in impatient customers only during K-vacations

100%

Sivasamy R.

Statistics in Transition new series

2024

vol. 25

issue 3

187-196

We investigate a matrix analysis study for a single-server Markovian queue with finite capacity, i.e. an M/M/1/N queue, where the single server can go for a maximum, i.e. a K number of consecutive vacation periods. During these vacation periods of the server, every customer becomes impatient and leaves the queues. If the server detects that the system is idle during service startup, the server rests. If the vacation server finds a customer after the vacation ends, the server immediately returns to serve the customer. Otherwise, the server takes consecutive vacations until the server takes a maximum number of vacation periods, e.g. K, after which the server is idle and waits to serve the next arrival. During vacation, customers often lose patience and opt for scheduled deadlines independently. If the customer’s service is not terminated before the customer’s timer expires, the customer is removed from the queue and will not return. Matrix analysis provides a computational form for a balanced queue length distribution and several other performance metrics. We design a ‘no-loss; no-profit cost model’ to determine the appropriate value for the maximum value of K consecutive vacation periods and provide a solution with a numerical illustration.

Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

75%

BOUCHENTOUF A. A., GUENDOUZI A., HOUALEF M., MAJID S.

Operations Research and Decisions

2022

vol. 32

issue 2

16-33

In this paper, we analyze an M/M/1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . . , K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system.

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1 Operations Research and Decisions

1 Statistics in Transition new series

1 BOUCHENTOUF A. A.

1 GUENDOUZI A.

1 HOUALEF M.

1 MAJID S.

1 Sivasamy R.

1 2024

1 2022

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A finite state Markovian queue to let in impatient customers only during K-vacations

Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience