On the Remaining Service Time upon Reaching a Given Level in M/G/1 Queues
Queueing Systems: Theory and Applications
The oscillating queue with finite buffer
Performance Evaluation
Duration of the buffer overflow period in a batch arrival queue
Performance Evaluation
Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Consecutive customer losses in regular and oscillating MX/G/1/n systems
Queueing Systems: Theory and Applications
On the statistical structure of losses caused by the buffer overflow
TELE-INFO'05 Proceedings of the 4th WSEAS International Conference on Telecommunications and Informatics
Buffer overflow period in a constant service rate queue
TELE-INFO'06 Proceedings of the 5th WSEAS international conference on Telecommunications and informatics
Remarks on the remaining service time upon reaching a target level in the M/G/1 queue
Operations Research Letters
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The distribution of the remaining service time upon reaching some target level in an M/G/1 queue is of theoretical as well as practical interest. In general, this distribution depends on the initial level as well as on the target level, say, B. Two initial levels are of particular interest, namely, level “1” (i.e., upon arrival to an empty system) and level “B−1” (i.e., upon departure at the target level).In this paper, we consider a busy cycle and show that the remaining service time distribution, upon reaching a high level B due to an arrival, converges to a limiting distribution for B→∞. We determine this asymptotic distribution upon the “first hit” (i.e., starting with an arrival to an empty system) and upon “subsequent hits” (i.e., starting with a departure at the target) into a high target level B. The form of the limiting (asymptotic) distribution of the remaining service time depends on whether the system is stable or not. The asymptotic analysis in this paper also enables us to obtain good analytical approximations of interesting quantities associated with rare events, such as overflow probabilities.