IEEE/ACM Transactions on Networking (TON)
Effective bandwidths for multiclass Markov fluids and other ATM sources
IEEE/ACM Transactions on Networking (TON)
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Multiservice Loss Models for Broadband Telecommunication Networks
Multiservice Loss Models for Broadband Telecommunication Networks
Queues with Service Rate Controlled by a Delayed Feedback
Queueing Systems: Theory and Applications
MAMSolver: A Matrix Analytic Methods Tool
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Insensitive Bandwidth Sharing in Data Networks
Queueing Systems: Theory and Applications
Steady-state analysis of a queue with varying service rate
Steady-state analysis of a queue with varying service rate
Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times
Queueing Systems: Theory and Applications
BOUNDS FOR FLUID MODELS DRIVEN BY SEMI-MARKOV INPUTS
Probability in the Engineering and Informational Sciences
Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates
Queueing Systems: Theory and Applications
M/M/C queues with Markov modulated service processes
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Erlang loss queueing system with batch arrivals operating in a random environment
Computers and Operations Research
Optimal robust policies for bandwidth allocation and admission control in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Queues where customers of one queue act as servers of the other queue
Queueing Systems: Theory and Applications
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Performance Evaluation
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In this paper, we consider a queue whose service speed changes according to an external environment that is governed by a Markov process. It is possible that the server changes its service speed many times while serving a customer. We derive first and second moments of the service time of customers in system using first step analysis to obtain an insight on the service process. In fact, we obtain an intriguing result in that the moments of service time actually depend on the arrival process! We also show that the mean service rate is not the reciprocal of the mean service time.Further, since it is not possible to obtain a closed form expression for the queue length distribution, we use matrix geometric methods to compute performance measures such as average queue length and waiting time. We apply the method of large deviations to obtain tail distributions of the workload in the queue using the concept of effective bandwidth. We present two applications in computer systems: (1) Web server with multi-class requests and (2) CPU with multiple processes. We illustrate the analysis and various methods discussed with the help of numerical examples for the above two applications.