##
**Heuristic solution for the optimal thresholds in a controllable multi-server heterogeneous queueing system without preemption.**
*(English)*
Zbl 1390.90209

Vishnevsky, Vladimir (ed.) et al., Distributed computer and communication networks. 18th international conference, DCCN 2015, Moscow, Russia, October 19–22, 2015. Revised selected papers. Cham: Springer (ISBN 978-3-319-30842-5/pbk; 978-3-319-30843-2/ebook). Communications in Computer and Information Science 601, 238-252 (2016).

Summary: As it known the optimal policy which minimizes the long-run average cost per unit of time in a multi-server queueing system with heterogeneous servers without preemption has a threshold structure. It means that the slower server must be activated whenever all faster servers are busy and the number of customers in the queue exceeds some specified for this server threshold level. The optimal thresholds can be evaluated using the Howard iteration algorithm or by minimizing the function of the average cost which can be obtained in closed form as a function of unknown threshold levels. The both cases have sufficient restrictions on dimensionality of the model. In present paper we provide a heuristic method to derive expressions for the optimal threshold levels in explicit form as functions of system parameters like service intensities, usage and holding costs for an arbitrary number of servers. The proposed method is based on the fitting of the boundary planes between the areas where the optimal
threshold takes a certain value.

For the entire collection see [Zbl 1377.68015].

For the entire collection see [Zbl 1377.68015].

### MSC:

90B22 | Queues and service in operations research |

### Keywords:

controllable queueing system; heterogeneous servers; long-run average cost; threshold policy; optimal allocation
PDF
BibTeX
XML
Cite

\textit{D. Efrosinin} and \textit{V. Rykov}, Commun. Comput. Inf. Sci. 601, 238--252 (2016; Zbl 1390.90209)

Full Text:
DOI

### References:

[1] | 1.Aviv, Y., Federgruen, A.: The value-iteration method for countable state Markov decision processes. Oper. Res. Lett. 24(5), 223-234 (1999) · Zbl 0954.90060 |

[2] | 2.Efrosinin, D.: Controlled Queueing Systems with Heterogeneous Servers. Dynamic Optimization and Monotonicity Properties. VDM Verlag, Saarbrücken (2008) |

[3] | 3.Efrosinin, D.: Queueing model of a hybrid channel with faster link subject to partial and complete failures. Ann. Oper. Res. 202(1), 75-102 (2013) · Zbl 1263.90023 |

[4] | 4.Efrosinin, D., Rykov, V.: On performance characteristics for queueing systems with heterogeneous servers. Autom. Remote Control 69(1), 61-75 (2008) · Zbl 1156.93028 |

[5] | 5.Howard, R.: Dynamic Programming and Markov Processes. Wiley Series, New York (1960) · Zbl 0091.16001 |

[6] | 6.Kumar, B.K., Arivudainambi, D.: Transient solution of an · Zbl 0962.60096 |

[7] | 7.Puterman, M.L.: Markov Decision Process. Wiley Series in Probability and Mathematical Statistics. Wiley, New York (1994) |

[8] | 8.Rykov, V., Efrosinin, D.: Optimal control of queueing systems with heterogeneous servers. Queueing Syst. 46, 389-407 (2004) · Zbl 1061.90035 |

[9] | 9.Rykov, V., Efrosinin, D.: On the slow server problem. Autom. Remote Control 70(12), 2013-2023 (2009) · Zbl 1180.90078 |

[10] | 10.Sennott, L.I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999) · Zbl 0997.93503 |

[11] | 11.Tijms, H.C.: Stochastic Models. An Algorithmic Approach. Wiley, New York (1994) · Zbl 0838.60075 |

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.