A finite M/T-SPH/1/N queueing model with variable arrival rate is analyzed,where T-SPH denotes the infinite phase type distribution defined on a birth and death process with countably many states.For an arriving customer the probability he decides join the queue depends on the number of customers present in the system.For the queueing system,the established QBD process model can be analyzed by the method of generalized eigenvalues.Using this method,the expression of stationary queue length distribution of the queue is given.Furthermore,the obtained results enable us to give the matrix-geometric solution of the QBD process.Finally,several numerical examples are also presented to illustrate the impact of parameters on performance indexes of the queueing system.
关键词
M/T-SPH/1/N排队/有限排队/QBD过程/谱展开方法/矩阵几何解
Key words
the M/T-SPH/1/N queue/finite queue/QBD process/spectral expansion method/matrix-geometric solution
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