A matrix continued fraction approach to multiserver retrial queues

We consider basic M/M/c/c (c≥1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c retrial queues with large value of c.

[1]  Jesus R. Artalejo,et al.  Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue , 2002, Ann. Oper. Res..

[2]  S. N. Stepanov,et al.  Markov models with retrials: The calculation of stationary performance measures based on the concept of truncation , 1999 .

[3]  Alexander N. Dudin,et al.  A Retrial BMAP/PH/N System , 2002, Queueing Syst. Theory Appl..

[4]  Wyman Fair.  Noncommutative Continued Fractions , 1971 .

[5]  Bin Liu,et al.  Analyzing retrial queues by censoring , 2010, Queueing Syst. Theory Appl..

[6]  Yutaka Takahashi,et al.  PERFORMANCE ANALYSIS OF OPTICAL BURST SWITCHED NETWORKS WITH LIMITED-RANGE WAVELENGTH CONVERSION, RETRANSMISSION AND BURST SEGMENTATION , 2009 .

[7]  Jesús R. Artalejo,et al.  Retrial Queueing Systems: A Computational Approach , 2008 .

[8]  Marco Ajmone Marsan,et al.  Efficient estimation of call blocking probabilities in cellular mobile telephony networks with customer retrials , 2001, IEEE J. Sel. Areas Commun..

[9]  Attahiru Sule Alfa,et al.  PCS networks with correlated arrival process and retrial phenomenon , 2002, IEEE Trans. Wirel. Commun..

[10]  Jesús R. Artalejo,et al.  Retrial Queueing Systems , 2008 .

[11]  Antonio Gómez-Corral,et al.  A bibliographical guide to the analysis of retrial queues through matrix analytic techniques , 2006, Ann. Oper. Res..

[12]  A. Hessel,et al.  Convergence of Noncommutative Continued Fractions , 1975 .

[13]  Yutaka Takahashi,et al.  State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment , 2010 .

[14]  Peter G. Taylor,et al.  Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes , 1995 .

[15]  Wuyi Yue,et al.  Proceedings of the 5th International Conference on Queueing Theory and Network Applications , 2010 .

[16]  Yutaka Takahashi,et al.  M/M/3/3 and M/M/4/4 retrial queues , 2009 .

[17]  Thomas Hanschke.  Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts , 1987 .

[18]  XQ Yang,et al.  Journal of industrial and management optimization (Volume 1) , 2005 .

[19]  Jesus R. Artalejo,et al.  On the impact of customer balking, impatience and retrials in telecommunication systems , 2009, Comput. Math. Appl..

[20]  Jesús R. Artalejo,et al.  Approximation of multiserver retrial queues by means of generalized truncated models , 2002 .

[21]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[22]  Vicent Pla,et al.  Generalized Truncated Methods for an Efficient Solution of Retrial Systems , 2008 .

[23]  Marcel F. Neuts,et al.  Numerical investigation of a multiserver retrial model , 1990, Queueing Syst. Theory Appl..

[24]  Hendrik Baumann,et al.  Numerical solution of level dependent quasi-birth-and-death processes , 2010, ICCS.

[25]  Annie A. M. Cuyt,et al.  Handbook of Continued Fractions for Special Functions , 2008 .

[26]  Технология.  Springer Science+Business Media , 2013 .

[27]  Avishai Mandelbaum,et al.  Queueing Models of Call Centers: An Introduction , 2002, Ann. Oper. Res..

[28]  Phuoc Tran-Gia,et al.  Modeling of Customer Retrial Phenomenon in Cellular Mobile Networks , 1997, IEEE J. Sel. Areas Commun..

[29]  T. Hanschke,et al.  A matrix continued fraction algorithm for the multiserver repeated order queue , 1999 .

[30]  Jesus R. Artalejo,et al.  Cellular mobile networks with repeated calls operating in random environment , 2010, Comput. Oper. Res..

[31]  J. Templeton.  Retrial queues , 1999 .

[32]  Bara Kim,et al.  MAP1, MAP2/M/c retrial queue with guard channels and its application to cellular networks , 1999 .

[33]  Wyman Fair.  A convergence theorem for noncommutative continued fractions , 1972 .

[34]  Yutaka Takahashi,et al.  A simple algorithm for the rate matrices of level-dependent QBD processes , 2010, QTNA.

[35]  Alexander N. Dudin,et al.  Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory , 2006, Queueing Syst. Theory Appl..

[36]  Fikri Karaesmen,et al.  The impact of retrials on call center performance , 2004, OR Spectr..