Bernoulli feedback queue with slow service period and impatient customers
1.School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China; 2.Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China)
Abstract：Consider an M／M／1 queue with impatient customers and Bernoulli feedback in a two-phase (fast and slow) random enviroment. The system resides in a twophase exponentially distributed random time, and the service time in two phases is subject to exponential distribution. When the system is in the slow phase, customers become impatient and activate a timer subject to exponential distribution. If the system′s environment does not change from slow to fast until the expiration of the timer, the customer will abandon the queue and never return again. Just after completion of his service, a customer may leave the system with probabilty σ(0<σ≤1), or feedback with probability 1-σ. From the system′s equilibrium equations, we build a differential equation about the probabilty generating function of queuelength, and derive the result by using analytic solutions. In addition, we also derive the mean queue size from another equilibrium equation.
2010, Vol. 31 
