Bandwidth allocation in wireless networks with guaranteed packet-loss performance
IEEE/ACM Transactions on Networking (TON)
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
The Nonpreemptive Priority Map/G/1 Queue
Operations Research
The M/G/1 FIFO Queue with Several Customer Classes
Queueing Systems: Theory and Applications
Multiclass Markovian fluid queues
Queueing Systems: Theory and Applications
M/M/∞ queues in semi-Markovian random environment
Queueing Systems: Theory and Applications
Erlang loss queueing system with batch arrivals operating in a random environment
Computers and Operations Research
Queues where customers of one queue act as servers of the other queue
Queueing Systems: Theory and Applications
An infinite-server queue influenced by a semi-Markovian environment
Queueing Systems: Theory and Applications
Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes
Computers and Operations Research
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This paper considers single-server queues with several customer classes. Arrivals of customers are governed by the underlying continuous-time Markov chain with finite states. The distribution of the amount of work brought into the system on arrival is assumed to be general, which may differ with different classes. Further, the service speed depends on the state of the underlying Markov chain. We first show that given such a queue, we can construct the corresponding new queue with constant service speed by means of a change of time scale, and the time-average quantities of interest in the original queue are given in terms of those in the new queue. Next we characterize the joint distribution of the length of a busy period and the number of customers served during the busy period in the original queue. Finally, assuming the FIFO service discipline, we derive the Laplace--Stieltjes transform of the actual waiting time distribution in the original queue.