zbMATH — the first resource for mathematics

Queueing models for a flexible machining station. II: The method of Coxian phases. (English) Zbl 0553.90050
[For part I see the preceding review.] - A work station of a flexible manufacturing system (FMS) is modeled as a multi-server queue with finite waiting room. The interarrival/service time distributions have squared coefficients of variations not less than 0.5 and are modeled as Coxian laws of two phases. A recursive scheme is developed to calculate the equilibrium queue length distribution. The model, together with the diffusion approximation model of part I, can be used to aid the design of FMS work stations.

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
Full Text: DOI
[1] Altiok, T., Approximate analysis of exponential tandem queues with blocking, European journal of operational research, 11, 390-398, (1982) · Zbl 0497.60096
[2] Altiok, T.; Stidham, S., The allocation of interstage buffer capacities in production lines, IIE transactions, 15, 292-299, (1983)
[3] Cox, D.R., A use of complex probabilities in the theory of stochastic processes, (), 313-319 · Zbl 0066.37703
[4] Herzog, U.; Woo, L.; Chandy, K.M., Solution of queueing problems by a recursive technique, IBM journal of research and development, 19, 295-300, (1975) · Zbl 0307.68043
[5] Keilson, J., Markov chain models: ratity and exponentiality, (1979), Springer New York
[6] Marie, R.A., An approximate analytical method for general queueing networks, IEEE transactions of software engineering, SE-5, 530-538, (1979) · Zbl 0422.90037
[7] Marie, R.A., Calculating equilibrium probabilities for ψ(n)/ck/1/N queue, (), 117-125
[8] Sauer, C.H.; Chandy, K.M., Approximate analysis of central server models, IBM journal of research and development, 19, 301-313, (1975) · Zbl 0302.68080
[9] Stewart, W.; Marie, R., A numerical solution for the ψ(n)/ck/r/N queue, European journal of operational research, 5, 56-68, (1980) · Zbl 0433.60094
[10] Sunaga, T.; Biswas, S.K.; Nishida, N., An approximation method using continuous models for queueing problems, II: multi-server finite queue, Journal of the operations research society of Japan, 25, 113-127, (1982) · Zbl 0487.60079
[11] Van Hoorn, M., Algorithms and approximations for queueing systems, () · Zbl 0541.60095
[12] Whitt, W., Approximating a point process by a renewal process, I: two basic methods, Operations research, 30, 125-147, (1982) · Zbl 0481.90025
[13] Whitt, W.; Whitt, W.; Whitt, W., Evaluating approximations for queues, I: extremal distributions, II (with J.G. klincewicz): shape constraints, III: mixtures of exponential distributions, AT&T Bell laboratories technical journal, AT&T Bell laboratories technical journal, AT&T Bell laboratories technical journal, 63, 163-175, (1984) · Zbl 0598.90042
[14] Wolff, R.W., Poisson arrivals see time averages, Operations research, 30, 223-231, (1982) · Zbl 0489.60096
[15] Yao, D.D., Queueing models of flexible manufacturing systems, () · Zbl 0649.90061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.