service rate per busy service is u Therefore over all service rate when there are n units in the system may be obtained in the following two situations i And If n s all the customers may be served simulataneously There will be no queue s n number of servers may remain idle and then Hn nu n 0 1 2 s ii If n s all the servers are busy maximum number of customers waiting in queue will be n s then nu MODEL IV B MMS NIFCFS In model IV A if the maximum number in the system is limited to N then as in model III sp P 0 2n P su Where Po may be written as sp n s 1 p sp sp n s Virtually the same relationships hold between P and Po as in model IV A with infinite capacity Therefore Po 51 s 1 for 0 n N forn N sp Pon for o n s S pr Po s 0 for n N n 1 nu for 0 n s for s n N for s n N SP sp s s s 1 sp n n n s 1 p s 1 1 1 p N s 1 p 1 This queueing modrl with limited waiting room is valuable because of its relevance to many real situations and the fact that changes may be made to its properties by adjusting the number of servers or the capacity of the waiting room However while poission arrivals are common in practice negative exponential service times are less so and it is the second assumption in the system MIMs that limits its usefulness Example