An Analytical Throughput Approximation for Closed Fork/Join Networks

References

• Bacelli F, Liu Z (1992) Comparison properties of stochastic decision free Petri nets. IEEE Trans. Automatic Control 37(12):1905–1920.Crossref, Google Scholar
• Bacelli F, Makowski AM, Shwartz A (1989) The fork/Join queue and related systems with synchronization constraints: Stochastic ordering and computable bounds. Adv. Appl. Probab. 21(3):629–660.Crossref, Google Scholar
• Baskett F, Chandy KM, Muntz RR, Palacios FG (1975) Open, closed, and mixed networks of queues with different classes of customers. J. Assoc. Comput. Machinery 22(2):248–260.Crossref, Google Scholar
• Baynat B, Dallery Y (1995) Approximate analysis of multi-class synchronized closed queueing networks. Proc. Internat. Workshop Modeling, Anal., Simulation Comput. Telecom. Systems (Durham, NC), 23–27.Crossref, Google Scholar
• Baynat B, Dallery Y (2000) An approximation method for general closed queueing networks with fork/join mechanisms. J. Oper. Res. Soc. 51(2):198–208.Crossref, Google Scholar
• Bolch G, Greiner S, de Meer H, Trivedi KS (2006) Queueing Networks and Markov Chains (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Chandy KM, Herzog U, Woo L (1975) Parametric analysis of queueing networks. IBM J. Res. Development 51:36–42.Crossref, Google Scholar
• Di Mascolo M, Frein Y, Dallary Y (1996) An analytical method for performance evaluation of kanban controlled production systems. Oper. Res. 44(1):50–64.Link, Google Scholar
• Duda A (1988) Approximate performance analysis of parallel systems. Iazeolla G, Courtois PJ, Boxma OJ, eds. Computer Performance and Reliability (North-Holland, Amsterdam), 189–202.Google Scholar
• Duenyas I (1994) Estimating the throughput of cyclic assembly systems. Internat. J. Production Res. 32(6):1403–1419.Crossref, Google Scholar
• Duenyas I, Hopp WJ (1990) Estimating variance of throughput from cyclic exponential queueing systems. Queueing Systems 7(3–4):337–354.Crossref, Google Scholar
• Duenyas I, Hopp WJ (1992) CONWIP assembly with deterministic processing and random outages. IIE Trans. 24(4):97–109.Crossref, Google Scholar
• Duenyas I, Hopp WJ (1993) Estimating the throughput of an exponential CONWIP assembly systems. Queueing Systems 14(1–2):135–157.Crossref, Google Scholar
• Harrison JM (1973) Assembly-like queues. J. Appl. Probab. 10(2):354–367.Crossref, Google Scholar
• Hopp JM, Simon JT (1989) Bounds and heuristics for assembly-like queues. Queueing Systems 4(2):137–156.Crossref, Google Scholar
• Ko SS, Serfozo RF (2004) Response times in M/M/s fork-join networks. Adv. Appl. Probab. 36(3):854–871.Crossref, Google Scholar
• Kouvatsos DD (1994) Entropy maximisation and queueing network models. Ann. Oper. Res. 48(1):63–126.Crossref, Google Scholar
• Kouvatsos DD, Georgatsos PH, Tabet-Aouel NM (1989) A universal maximum entropy algorithm for general multiple class open networks with mixed service disciplines. Puigjaner R, Potier D, eds. Modelling Techniques and Tools for Computer Performance Evaluation (Plenum, New York), 397–419.Crossref, Google Scholar
• Krishnamurthy A, Suri R (2006) Performance analysis of single stage kanban controlled production systems using parametric decomposition. Queueing Systems 54(2):141–161.Crossref, Google Scholar
• Krishnamurthy A, Suri R, Vernon M (2003) Two-moment approximations for throughput and mean queue length of a fork/join station with general input process. Shanthikumar JG, Yano DD, Zijm WHM, eds. Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains (Kluwer Academic Publishers, New York), 87–126.Crossref, Google Scholar
• Krishnamurthy A, Suri R, Vernon M (2004) Analysis of a fork/join synchronization station with inputs from Coxian servers in a closed queuing network. Ann. Oper. Res. 125(1):69–94.Crossref, Google Scholar
• Latouche G (1981) Queues with paired customers. J. Appl. Probab. 18(3):684–696.Crossref, Google Scholar
• Liu YC, Perros HG (1991) Approximate analysis of a closed fork/join model. Eur. J. Oper. Res. 53(3):382–392.Crossref, Google Scholar
• Marie R (1979) An approximate analytical method for general queueing networks. IEEE Trans. Software Engrg. 5(5):530–538.Crossref, Google Scholar
• Nelson R, Tantawi AN (1988) Approximate analysis of fork/join synchronization in parallel queues. IEEE Trans. Comput. 37(6):739–743.Crossref, Google Scholar
• Prabhakar B, Bambos N, Mountford TS (2000) The synchronization of Poisson processes and queueing networks with service and synchronization nodes. Adv. Appl. Probab. 32(3):824–843.Crossref, Google Scholar
• Rao PC, Suri R (1994) Approximate queueing network models of fabrication assembly systems: Part I—Single level systems. Production Oper. Management 3(4):244–275.Crossref, Google Scholar
• Rao PC, Suri R (2000) Performance analysis of an assembly station with input from multiple fabrication lines. Production Oper. Management 9(3):283–302.Crossref, Google Scholar
• Sadre R, Haverkort BR, Reinelt P (2007) A fixed-point algorithm for closed queueing networks. Proc. 4th Eur. Performance Engrg. Conf. Formal Methods Stochastic Models for Performance Evaluation (Springer, Berlin), 154–170.Crossref, Google Scholar
• Som P, Wilhelm WE, Disney RL (1994) Kitting process in a stochastic assembly system. Queueing Systems 17(3–4):471–490.Crossref, Google Scholar
• Sönmez E, Kekre S, Scheller-Wolf A, Secomandi N (2013) Strategic analysis of technology and capacity investments in the liquefied natural gas industry. Eur. J. Oper. Res. 226(1):100–114.Crossref, Google Scholar
• Takahashi M, Osawa T, Fujisawa T (1998) A stochastic assembly system with resume levels. Asia-Pasific J. Oper. Res. 15(2):127–146.Google Scholar
• Takahashi M, Osawa T, Fujisawa T (2000) On a synchronization queue with two finite buffers. Queueing Systems 36(1–3):107–123.Crossref, Google Scholar
• Varki E (1999) Mean value technique for closed fork-join networks. Proc. ACM SIGMETRICS Conf. Measurement Modeling Comput. Systems, Atlanta, GA, 103–112.Crossref, Google Scholar
• Whitt W (1983) The queueing network analyzer. Bell System Tech. J. 62(9):2816–2843.Google Scholar
• Whitt W (1984) Open and closed models for networks of queues. AT&T Bell Laboratories Tech. J. 63(9):1911–1979.Crossref, Google Scholar