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Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since.
In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field.
To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix-Analytic Methods in Queues 2 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.
This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
List of Notations
Preface
Single-Server Queues Embedded at Departure Epochs
BMAP/G/1 queue
MAP/G/1 queue
PH/G/1 queue
M/G/1 queue
PH/M/1 queue
M/M/1 queue
Exercises
Single-Server Queues Embedded at Arrival Epochs
GI/PH/1 queue
GI/M/1 queue
M/PH/1 queue
M/M/1 queue
Exercises
Single-Server Queues Based on Arbitrary Epochs
BMAP/PH/1 queue
MAP/PH/1 queueing model
PH/PH/1 queue
PH/M/1 queue
M/PH/1 queue
M/M/1 queue
Exercises
Busy Period in Queues
Busy period in M/G/1-type queues (scalar case)
Busy period in M/G/1-type queues (matrix case)
Busy period in GI/M/1-type queues (scalar case)
Busy period in GI/PH/1-type queues
BMAP/PH/1 queue
Busy period in QBD-type queues
When the fundamental period is not the busy period
GI/G/1 queues
Exercises
Multi-Server Queues
BMAP/PH/c queue
MAP/PH/3 queue
BMAP/M/c queue
MAP/M/c queue
M/M/c queue
GI/PH/c queue
Exercises
Finite-Capacity Queues
Finite-capacity queues with single server
BMAP/PH/1/K queue
MAP/PH/1/K queue
PH/M/1/K queue
M/PH/1/K queue
M/M/1/K queue
Finite-capacity queues with multiple servers
BMAP/M/c/K queue
MAP/M/c/K queue
PH/M/c/K queue
M/M/c/K queue
Exercises
Simulation
Introduction to ARENA
Model building using ARENA
GI/G/c queues
ARENA modules for GI/G/c queues
Validation of GI/G/1 queues
Simulated examples for GI/G/1 queues
Validation of GI/G/c queues
Simulated examples of GI/G/c queues
BMAP/G/c queues
ARENA modules for BMAP/G/c queues
Validation of BMAP/G/1 queues
Simulated examples for BMAP/G/1 queues
Validation of BMAP/M/c queues
Simulated examples for BMAP/G/c queues
Exercises
References
Index