A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations.
Bouchentouf, Amina A. and Sakhi, Hanane
A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
1, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol10/iss1/1