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B. (B)MAP/PH/1 queues
A MAP/PH/1 represents a single server queue that has MAP arrival process
and PH service process. The MAP/PH/1 queue is a quasi
birthdeath process whose matrices can be computed using the matrix
parameters that define the MAP and the PH processes of the MAP/PH/1
queue. Let the MAP describtors to be
of order
and the PH service time parameters to be
of order
. The infinitesimal generator matrix
for the
corresponding MAP/PH/1 queue has a structure given by

(B.1) 
where each of its matrices is defined as follows

(B.2) 
where
is the order identity matrix,
, and denotes the Kroneker product.
A BMAP/PH/1 represent a single server queue that has BMAP arrival process and
PH service process. The BMAP/PH/1 queue results in a M/G/1type process.
Let the BMAP parameteres be
for and PH parameters be
of order and , respectively. The infinitesimal
generator matrix
for the corresponding BMAP/PH/1 queue
is given by

(B.3) 
where each of its matrices is defined as follows

(B.4) 
where
is the order identity matrix,
, and denotes the Kroneker product.
Next: C. NewtonRaphson Fitting Technique
Up: Aggregate matrixanalytic techniques and
Previous: A. FeldmanWhitt Fitting Algorithm
Alma Riska
20030113