Stability Conditions for Retrial Queueing Systems with Regenerative Input Flow

Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers

“…We consider the system S 2 . For the sake of brevity, assume that r = 2, that is, the distribution of the service time has two exponential phases so that the service time η has the form η = η (1) + η (2) .…”

“…The random variables η (1) and η (2) are independent and have exponential distributions with rates μ 1 and μ 2 , respectively. Our approach may also be used for models with r > 2, but calculations are too cumbersome to give them here.…”

“…The set of states K 3 = ((0, 1), (0, 2), (1,1), (1,2), (2,2)). We put x 1 = P (0,1) , x 2 = P (0,2) , x 3 = P (1,1) , x 4 = P (1,2) , x 5 = P (2,2) .…”

“…(2) C λ (1) C ; therefore, the phase-type service is better than exponentially distributed service time under the assumption that they have the same mean service time.…”

“…The method suggested in this paper allows us to conduct the asymptotic analysis of a wide set of queueing models including retrial systems [1], priority systems as well as various generalizations of the systems with interruptions of service [4,5].…”