Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

retrial queue

Heavy outgoing call asymptotics for MMPP|M|1 retrial queue with two way communication and multiple types of outgoing calls

In this paper, we consider a single server retrial queue MMPP|M|1 with two way communication and multiple types of outgoing calls. Calls received by the system occupy the device for operating, if it is free, or are sent to orbit, where they make a random delay before the next attempt to occupy the device. The duration of the delay has an exponential distribution. The main issue of this model is an existence of various types of outgoing calls in the system. The intensity of outgoing calls is different for different types of outgoing calls.

Output process of the M|GI|1 is an asymptotical renewal process

Most of the studies on models with retrials are devoted to the research of the number of applications in the system or in the source of repeated calls using asymptotic and numerical approaches or simulation. Although one of the main characteristics that determines the quality of the communication system is the number of applications served by the system per unit of time. Information on the characteristics of the output processes is of great practical interest, since the output process of one system may be incoming to another.

Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed.