Stability of Nested Queue Model With Finite Waiting Capacity

Anju Bhatt, Jaejin Jang


Abstract: The paper describes a mathematical model to identify the conditions of stability for a two stage nested queue model. We envisioned the two stages as two stations in a hospital that a patient passes through before completing service. In the first station there are two servers (i.e., nurses) which attend to the patient. When a patient arrives to the first station he/she is served by one of the two servers, the server serves the patient and stays with the customer until the service in the second station of the model is completed. In the second station, another server (i.e., doctor) attends to the customer with the cooperation of first station server. The service rates of the servers and arrival rates of the patients follow exponential distribution. The mathematical model is also used to determine the conditions that allow the patients in system to be served effectively. To estimate the conditions of stability, the steady state probabilities have been calculated and stability behavior has been given for special cases.


Nested queue; Steady state; Probability; Stability

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Hunt, G. C. (1956). Sequential arrays of waiting lines. Operation Researc, 4, 674–683.

Konheim, A. G., & Reiser, M. (1976). A queueing model with finite waiting room and blocking. Journal of the Association for Computing Machinery, 23(2), 328-341.

Modi, J. A. (1974). A nested queue model for the analysis of air traffic control sectors. Transportation Research, 8, 219-224.

Perros, H. G., & Foster, F. G. (1980). On the blocking process in queue networks. European Journal of Operational Research, 5, 276-283.

Perros, H. G. (1981). A two-level open queue network with blocking and feedback. RAIRO-Operations Research-Recherche Opérationnelle, 15(1), 27-38.

Perros, H. G. (1994). Queueing networks with blocking–exact and approximate solutions. Oxford Press.

Grassmann, W. K., & Tavakoli, J. (2005). Two station queueing networks with moving servers, blocking, and customer. Electronic Journal of Linear Algebra, 13, 72-89.




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