Limited-1 cyclic service system as an imbedded Markov chain at server arrival instants

The authors model the limited-1 cyclic service system as an embedded Markov chain at server arrival instants. Using the related state equations, for a system with (N+1)-queues, a set of (N+1) simultaneous equations in (N+1) unknowns is derived whose solution gives the probability of queue i for i=0,1, . . .,N being empty when the server arrives there. An expression of the expected number of customers waiting at a queue when the server arrives there, is also derived. This expression contains, besides these probabilities, terms which still remain to be evaluated. Therefore, as an interim measure, a numerical iterative approach, appropriate for systems with small number of queues, is used. Also calculated are the average waiting times at each queue. Some numerical examples are presented to validate this approach.<>