Two-channel MAP/PH/2 system with customer resequencing

Abstract

Consideration was given to the two-server queuing system with resequencing buffer and customer resequencing to which a Markov customer flow arrives. The resequencing buffer has also an infinite capacity. The time of customer servicing by each server has the same phasetype distribution. A recurrent algorithm was proposed for calculation of the joint stationary distribution of the numbers of customers in the buffer and resequencing buffer. The stationary distributions of the customer sojourn time in the system and resequencing buffer were obtained in terms of the Laplace–Stieltjes transform in the form of infinite sums. Examples of calculations of the established relations were given.