Approximations for waiting time in GI/G/1 systems
Queueing Systems: Theory and Applications
An interpolation approximation for the mean workload in a GI/G/1 queue
Operations Research
Exact and approximate numerical solutions of steady-state distributions arising in the queue GI/G/1
Queueing Systems: Theory and Applications - Numerical computations in queues
End-to-end packet delay and loss behavior in the internet
SIGCOMM '93 Conference proceedings on Communications architectures, protocols and applications
Numerical approximations for the steady-state waiting times in a GI/G/1 queue
Queueing Systems: Theory and Applications
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Detecting Conflicts of Interest
RE '06 Proceedings of the 14th IEEE International Requirements Engineering Conference
A conditional probability approach to M/G/1-like queues
Performance Evaluation
Performance evaluation of a single node with general arrivals and service
ASMTA'11 Proceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications
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We propose a simple approximation to assess the steady-state probabilities of the number of customers in Ph/Ph/1 and Ph/Ph/1/N queues, as well as probabilities found on arrival, including the probability of buffer overflow for the Ph/Ph/1/N queue. The phase-type distributions considered are assumed to be acyclic. Our method involves iteration between solutions of an M/Ph/1 queue with state-dependent arrival rate and a Ph/M/1 queue with state-dependent service rate. We solve these queues using simple and efficient recurrences. By iterating between these two simpler models our approximation divides the state space, and is thus able to easily handle phase-type distributions with large numbers of stages (which might cause problems for classical numerical solutions). The proposed method converges typically within a few tens of iterations, and is asymptotically exact for queues with unrestricted queueing room. Its overall accuracy is good: generally within a few percent of the exact values, except when both the inter-arrival and the service time distributions exhibit low variability. In the latter case, especially under moderate loads, the use of our method is not recommended.