Whitt, Ward Approximations for departure processes and queues in series. (English) Zbl 0563.60094 Nav. Res. Logist. Q. 31, 499-521 (1984). The author provides a theoretical framework for approximating the departure process from a single-server queue and the congestion measures for single-server queues in series. Three methods, which are modifications of the asymptotic method and stationary-interval method, are indicated by which the approximations might be improved. Reviewer: R.Subramian Cited in 23 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:approximating the departure process; single-server queues in series PDF BibTeX XML Cite \textit{W. Whitt}, Nav. Res. Logist. Q. 31, 499--521 (1984; Zbl 0563.60094) Full Text: DOI References: [1] ”Approximating Queues with Superposition Arrival Processes,” Ph.D. dissertation, Department of Industrial Engineering and Operations Research, Columbia University, 1981. [2] ”Approximating a point process by a renewal process. II: superposition arrival processes to queues,” Operations Research, 32 (1984), in press. · Zbl 0547.90034 [3] Berman, Advances in Applied Probability 15 pp 657– (1983) [4] ”Simulation Models of Satellite Airport Systems,” Ph.D. dissertation, Cornell University, 1972. [5] Introduction to Queueing Theory, 2nd ed., North-Holland, New York, 1981. [6] Daley, Advances in Applied Probability 8 pp 395– (1976) [7] Queueing Networks and Applications, Johns Hopkins University Press, Baltimore, in press. [8] ”Approximate Techniques for the Analysis of Tandem Queueing Systems,” Ph.D. dissertation, Department of Industrial Engineering, Clemson University, 1971. [9] , , and , Queues and Point Processes, Akademie-Verlag, Berlin, 1981. [10] Friedman, Operation Research 13 pp 121– (1965) [11] and , Analysis and Synthesis of Computer Systems, Academic, New York, 1980. [12] and , Limit Distributions for Sums of Independent Random Variables, 2nd ed., Addison-Wesley, Reading, MA, 1968. [13] Green, Operations Research 30 pp 210– (1982) [14] Lglehart, Advances in Applied Probability 2 pp 355– (1970) [15] and , ”Approximate formulae for the delay in the queueing system Gl/G/l,” Congressbook, Eighth International Teletraffic Congress, Melbourne, 235, 1–8, 1976. [16] Kuehn, IEEE Transactions in Communications 27 pp 113– (1979) [17] ”Estimating the delay in series queues,” Graduate School of Business, the University of Toledo, Toledo, Ohio, 1981. [18] Marshall, Operations Research 16 pp 651– (1968) [19] Melamed, Advances in Applied Probability 11 pp 422– (1979) [20] ”A Simulation Study and Analysis of a Two-Station, Waiting-Line Network Model,” Ph.D. dissertation, UCLA, 1965. [21] Rosenshine, Operations Research 23 pp 1155– (1975) [22] , , and , ”Improving approximations of aggregated queueing network subsystems. Computer Performance,” and , Eds., North-Holland, Amsterdam, 1977, pp. 1–22. [23] Shimshak, Naval Research Logistics Quarterly 26 pp 499– (1979) [24] ”The interchangeability of tandem. /M/1 queues in series,” Journal of Applied Probability, 690–695 (1979). · Zbl 0417.60091 [25] Whitt, Management Science 27 pp 619– (1981) [26] Whitt, Operations Research 30 pp 125– (1982) [27] Whitt, Operations Research Letters 2 pp 7– (1982) [28] Whitt, Bell System Technical Journal 62 pp 2779– (1983) [29] Whitt, Bell System Technical Journal 62 pp 2817– (1983) [30] ”The best order for queues in series,” Management Science, in press. · Zbl 0609.90045 [31] ”Departures from a queue with many busy servers,” Mathematics of Operations Research, 9 (1984), in press. · Zbl 0553.90044 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.