Time dependent of M M c N an with discouragement arrivals and retention of impatient customers

Abstract EN

In this paper, the matrix technique is employed to attain transient solution of a finite capacity multi-servers Markovian queue having discouraged arrivals, retention and reneging of reneged customers.

We consider the cases where both service times and the inter-arrival follow the exponential distribution.

The time dependent solution of the system is expressed by using the eigenvalues of a symmetric tridiagonal matrix.

As a reneged customer can be preserved in a lot of cases by utilizing definite convincing mechanisms to keep on queue for completion of service, it follows that a reneged customer can keep hold of the queuing system with chance.

Otherwise, customer may leave the queue without getting a service with probability (+=1).

Laplace transforms of governing equations system are expressed in matrix forms.

Moreover, employing the characteristics of symmetric tridiagonal matrices, and the steady state probabilities are gained.

Finally, some queuing models are derived as special cases of this system.