Abstract
This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain threshold L, low service rate is provided for cost saving. On the other hand, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L. The steady-state probability distribution and the expected number of customers in the system are derived. Through the first-step argument, a recursive algorithm for computing the first moment of the conditional sojourn time is obtained. Furthermore, employing the results of regeneration cycle analysis, the direct search method is also implemented to determine the optimal value of L for minimizing the long-run average cost rate function.
Highlights
In the classical queueing literature, the server is usually assumed to work at constant speed as long as there is any work present
Under the control of modified switching policy, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L
From the state-transition-rate diagram for the Geo/Geo/1 queue with service rate switching threshold, we can set up steady-state equations for Pi,0 and Pi,1 in the following:
Summary
In the classical queueing literature, the server is usually assumed to work at constant speed as long as there is any work present. With the assumption that the system capacity was limited, Wang and Tai [10] studied queue-dependent servers in the finite buffer M/M/3 queue with three types of service rate They constructed a relationship among the costs to determine the optimal queue lengths J and K of providing the second server and the third server, respectively. They found the best thresholds of queue length in activating servers and their corresponding service rate These studies greatly enhance the practical value of the multi-server queueing theory since it is realistic to consider the changes in the number of working servers. If the queue length reduces to less than the threshold, lower service rate is resumed Such model assumption means that the service rate can be switched countlessly in a regeneration cycle.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
