Journal of Computational and Applied Mathematics
Power series for stationary distributions of coupled processor models
SIAM Journal on Applied Mathematics
Boundary value problems in queueing theory
Queueing Systems: Theory and Applications
Queueing Models with Multiple Waiting Lines
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Analysis of cycle stealing with switching times and thresholds
Performance Evaluation
On the application of Rouché's theorem in queueing theory
Operations Research Letters
Analysis of a two-class FCFS queueing system with interclass correlation
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability β, and a customer of queue 2 is served with probability 1驴β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z 1,z 2) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z 1,z 2) in β. The first coefficient of this power series corresponds to the priority case β=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Padé approximation.