Analysis of the M/G/1 queue with discriminatory random order service policy

Authors:
Jeongsim Kim;Jerim Kim;Bara Kim
Affiliations:
Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk, 361-763, Republic of Korea;Department of Mathematics, Korea University 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea;Department of Mathematics, Korea University 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea
Venue:
Performance Evaluation
Year:
2011

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Abstract

We consider an M/G/1 queue with different classes of customers and discriminatory random order service (DROS) discipline. The DROS discipline generalizes the random order service (ROS) discipline: when the server selects a customer to serve, all customers waiting in the system have the same selection probability under ROS discipline, whereas customers belonging to different classes may have different selection probabilities under DROS discipline. For the M/G/1 queue with DROS discipline, we derive equations for the joint queue length distributions and for the waiting time distributions of each class. We also obtain the moments of the queue lengths and the waiting time of each class. Numerical results are given to illustrate our results.