We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the gener...

This paper analyzes an M/M/2 queueing system with two heterogeneous servers. Both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady st...

The use of a Markovian inventory system is critical part management. purpose this study to examine the demand for two commodities in system, one which designated as major item (Commodity-I) and other complimentary (Commodity-II). Demand arrives according Poisson process, service time exponential at queue-dependent rate. We investigate strategy (s,Q) type control commodity-I with random lead but...