Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Optimal two-threshold policies in an M/G/1 queue with two vacation types
Performance Evaluation
Analysis on queueing systems with synchronous vacations of partial servers
Performance Evaluation
Performance Analysis of a Queue with Congestion-Based Staffing Policy
Management Science
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In this paper, we study an M/M/c queue with a three threshold vacation policy denoted by (e, d, N). With such a policy, the servers keep serving the customers until the number of idle servers reaches d and then e of d servers start taking a vacation together. These e servers keep taking vacations until the number of customers in the system is at least N at a vacation completion instant, then the e servers return to serve the queue again. Using the matrix analytic method, we obtain the stationary performance measures and prove the conditional stochastic decomposition properties for the waiting time and queue length. This model is a generalization of previous multi-server vacation models and offers a useful performance evaluation and system design tool in multi-task server queueing systems.