An Analysis of the “Horizontal Y” Shaped Queuing Model to Assist in Health Care Institution

The “Horizontal Y” shaped queuing model in which there is bulk infinite arrival of patients, but available M services are limited. The discrete flow of patients in the system is reduced in continuous flow and a diffusion equation is used. In terms of means and variances of inter-arrival time distribution, this process of the number of patients and the number of servers is used, imposing reflecting boundaries. The inspiration for this analysis came from Aradhye and Kallurkar [2], and Armony [3], who explained that hospitals are complex systems whose problems can be resolved utilizing queuing theory. The present paper deals with a double-ended queue in which patients wait in a queue for services. The discrete distribution equations for queue size with various cases have been derived. Finally, the expected length of the queue, i.e., LC and the expected finite server, i.e., LS have been derived.