Sojourn Times in a Markovian Queue with Working Breakdowns and Delayed Working Vacations

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

Download Full-text

On a Markovian queue with weakly correlated interarrival times

Journal of Applied Probability ◽

10.1017/s0021900200097734 ◽

1981 ◽

Vol 18 (01) ◽

pp. 190-203 ◽

Cited By ~ 1

Author(s):

Guy Latouche

Keyword(s):

Time Distribution ◽

Queueing System ◽

Interarrival Time ◽

Probability Vector ◽

Common Value ◽

Markovian Queue ◽

The Stability ◽

Number Of Customers ◽

Stationary Probabilities ◽

Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

Download Full-text

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

Journal of the Operations Research Society of China ◽

10.1007/s40305-021-00361-w ◽

2021 ◽

Author(s):

Shakir Majid

Keyword(s):

Performance Analysis ◽

Impatient Customers ◽

Working Vacation ◽

Markovian Queue

Download Full-text

Sojourn times and the overtaking condition in Jacksonian networks

Advances in Applied Probability ◽

10.1017/s0001867800020218 ◽

1980 ◽

Vol 12 (04) ◽

pp. 1000-1018 ◽

Cited By ~ 10

Author(s):

J. Walrand ◽

P. Varaiya

Keyword(s):

Sojourn Time ◽

Sojourn Times ◽

Mutually Independent

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.

Download Full-text