Cost analysis of a queueing system with two service facilities

This paper studies the economic behaviour of a Markovian queueing system based upon the assumptions: (i) there is a regular service facility serving the units one by one, (ii) search for an additional service facility for the service of a group of units is started when the queue length increases to K (0<K<M, where M is the maximum waiting space), (iii) the search is dropped when the queue length reduces to a tolerable fixed size M-N, (iv) the time for arranging an additional service facility is a random variable. The model is directed towards finding the optimal operating policy (N,K) for a queueing system with a linear cost structure.