M/M/c/K state-dependent models for controlling the pilgrims and the design of hajj facilities

Abstract

In Hajj overflow of pilgrims causes queuing delay and in turn, is controlled by the capacity of facilities. The concept of flow control can be used to avoid the building of extreme queues. Thus, in this paper, a new analytical tool for measuring the performances of pilgrim movements in Hajj has been developed. The application of M/M/c/K queuing models for controlling the pilgrims and the design of facilities in Hajj is discussed. The paper also used some data on the flow of pilgrims for implementing the use of M/M/c/K queuing models for the above mentioned controlling and design. The result show that, the average number of pilgrims waiting in queue almost zero, because maybe most of the pilgrims only spend least then 12 second in the system.