Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Direct methods for sparse matrices
Direct methods for sparse matrices
Monte Carlo optimization, simulation, and sensitivity of queueing networks
Monte Carlo optimization, simulation, and sensitivity of queueing networks
Assembly-like queues with finite capacity: bounds, asymptotics and approximations
Queueing Systems: Theory and Applications
An approximate analysis for a class of assembly-like queues
Queueing Systems: Theory and Applications
Approximating nonstationary Ph(t)/Ph(t)/1/c queueing systems
Mathematics and Computers in Simulation
Some effects of nonstationarity on multiserver Markovian queueing systems
Operations Research
An investigation of phase-distribution moment-matching algorithms for use in queueing models
Queueing Systems: Theory and Applications
Rounding errors in certain algorithms involving Markov chains
ACM Transactions on Mathematical Software (TOMS)
Use of Polya distributions in approximate solutions to nonstationary M/M/s queues
Communications of the ACM - Special issue on simulation modeling and statistical computing
A discrete MAP/PH/1 queue with vacations and exhaustive time-limited service
Operations Research Letters
IEEE Transactions on Mobile Computing
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In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent values for the entire state probability vector. From this vector, most performance parameters such as expected waiting time and expected number in the system can be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of transient time. With these two solution methods one can examine any transient associated with the MAP(t)/PH(t)/1/K model including time-varying arrival and/or service patterns. Four test cases are used to demonstrate the effectiveness of these methods. Results from these cases indicate that both methods provide fast and accurate solutions to a wide range of transient scenarios.