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Accessible bibliography on retrial queues
MATHEMATICAL COMPUTER MODRLLING Mathematical and Computer Modelling 30 (1999) l-6
PERGAMON
www.elsevier.nl/locate/mcm
Accessible Bibliography on Retrial Queues J. R. ARTALEJO Departamento de Estadistica e I.O., Facultad de Matematicas Universidad Complutense de Madrid, 28040 Madrid, Spain j esus_artale johat . ucm.es Research
papers on retrial
queueing
systems
and their applications
have been published
in a va-
riety of mathematical and telecommunication journals, proceedings of international conferences, Ph.D. theses, and working papers of research institutions. Recently, Falin and Templeton published the first monograph
on retrial
queues, which gives a systematic
account
of the fundamental
methods and results on this topic. Some other books on queueing theory and stochastic systems, and several surveys also provide useful information about the existing results and open problems. It should also be noted that papers on retrial queues are published in many languages (we specially mention the Russian literature). The access to an English translation is often difficult or indeed impossible. Based on these observations, the author thought it might perhaps be useful to provide a bibliography including references easily accessible for the whole queueing community. To that end, the author in English. Of course, in translated
papers,
decided to include there is a certain
languages
other
than
only books and papers published in journals written subjectivity in this criterion, so readers interested English,
referred to the monograph by Falin and Templeton. The author is indebted to the people who helped
theses,
and proceedings
him by bringing
of conferences
are
new works of reference.
BOOKS 1. G.I. Falin and J.G.C. Templeton, Retrial Queues, Chapman and Hall, (1997). 2. V.G. Kulkami, Modeling and Analysis of Stochastic Systems, Chapman and Hall. (1995). 3. J. Riordan, Stochastic Service Systems, Wiley, (1962). 4. R. Syski, Introduction to Congestion Theory in Telephone Systems, North-Holland, (1986). 5. R.W. Wolff, Stochastic Modeling and the Theory of Queues, Prentince-Hall, (1989).
SURVEYS 1. J.R. Artalejo, Retrial queues with a finite number of sources, Journal of the Korean Mathematrcul Society 35, 503-525 (1998). 2. B.D. Choi and Y. Chang, Single server retrial queues with priority calls, Mathl. Cornput. Modelling (this issue). 3. G.I. Falin, Singleline repeated orders queueing systems, Optimization 17, 649-667 (1986). 4. G.I. Falin, A survey of retrial queues, Queveing Systems 7. 127-167 (1990). 5. V.G. Kulkami and H.M. Liang, Retrial queues revisited, In Rontiers in Queueing, (Edited by J.H. Dshalalow), pp. 19-34, CRC Press, (1997). 6. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2, 201-233 (1987); Correction, Queueing Systems 4, 94 (1989).
08957177/99/% - see front matter. P11:s0895-7177(99)00128-4
@ 1999 EIsevier Science Ltd. All rights reserved.
Typeset
by &+TE)c
2
J. R. ARTALEJO
MATHEMATICAL
JOURNALS
1. A. Aissani, Unreliable queueing with repeated orders, Microelectronics and Reliability 33, 2093-2106 (1993). 2. A. Aissani, A retrial queue with redundancy and unreliable server, Queueing Systems 17, 431-449 (1994). 3. A. Aissani and J.R. Artalejo, On the single server retrial queue subject to breakdowns, Queueing Systems 30, 309-321 (1998). 4. E. Altman and A.A. Borovkov, On the stability of retrial queues, Queueing Systems 26, 343-363 (1997). 5. V.V. Anisimov, Averaging methods for transient regimes in overloading retrial queueing systems, Mathl. Cornput. Modelling (this issue). 6. J.R. Artalejo, Explicit formulae for the characteristics of the M/Hz/l retrial queue, Jownal of the Operational Research Society 44, 309-313 (1993). 7. J.R. Artalejo, New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandicu 48, 23-36 (1994). 8. J.R. Artalejo and G.I. Falin, Stochastic decomposition for retrial queues, Top 2, 329-342 (1994). 9. J.R. Artalejo, A queueing system with returning customers and waiting line, Operations Research Letters 17, 191-199 (1995). 10. J.R. ArtaIejo and A. Gomez-Corral, Information theoretic analysis for queueing systems with quasi-random input, Mathl. Comput. Modelling 22 (3), 65-76 (1995). 11. J.R. Artalejo, Stationary analysis of the characteristics of the M/M/2 queue with constant repeated attempts, Opsearch 33, 83-95 (1996). 12. J.R. ArtaIejo and G.I. Falin, On the orbit characteristics of the M/G/l retrial queue, Naval Research Logistics 43, 1147-l 161 (1996). 13. J.R. Artalejo and A. Gomez-Corral, Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue, Journal of Applied Mathematics and Stochastic Analysis 9, 171-183 (1996). 14. J.R. Artalejo, Analysis of an M/G/l queue with constant repeated attempts and server vacations, Computers and Operations Research 24, 493-504 (1997). 15. J.R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated requests, Journal of Applied Probability 34, 223-233 (1997). 16. J.R. Artalejo and A. Gomez-Corral, Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals, OR Spektrum 20, 5-14 (1998). 17. J.R. Artalejo and A. Gomez-Corral, Analysis of a stochastic clearing system with repeated attempts, Stochastic Models 14, 623-645 (1998). 18. J.R. Artalejo and A. Gomez-Corral, On a single server queue with negative arrivals and request repeated, Journal of Applied Probability 38 (1999). 19. J.R. Artalejo and A. Gomez-Corral, Performance analysis of a single-server queue with repeated attempts, Mathl. Comput. Modelling (this issue). 20. J.R. ArtaIejo and A. Gomez-Corral. Computation of the limiting distribution in queueing systems with repeated attempts and disasters, RO-Recherche OpemtionnaIle/Opemtions Research (to appear). 21. P.P. Bocharov, 0.1. Pavlova and D.A. Puzikova, M/G/l/r retrial queueing systems with priority of primary customers, Mathl. Comput. Modelling (this issue). 22. B.D. Choi and K.K. Park, The M/G/l retrial queue with Bernoulli schedule, Queueing Systems 7, 219-227 (1990). 23. B.D. Choi, Y.W. Shin and W.C. Ahn. Retrial queues with collision arising from unslotted CSMA/CD protocol, Queueing Systems 11, 335-356 (1992). 24. B.D. Choi, D.H. Han and G.1. Falin, On the virtual waiting time for an M/G/l retrial queue with two types of calls, Journal of Applied Mathematics and Stochastic Analysis 6, 1 l-23 (1993). 25. B.D. Choi, K.K. Park and C.E.M. Pearce, An M/M/l retrial queue with control policy and general retrial times, Queueing Systems 14, 275-292 (1993). 26. 27. 28. 29. 30. 31. 32. 33. 34.
B.D. Choi, K.H. Rhee and K.K. Park, The ,M/G/l retrial queue with retrial rate control policy, Probability in the Engineering and Informational Sciences 7, 2s46 (1993). B.D. Choi, K.B. Choi and Y.W. Lee, M/G/l retrial queueing systems with two types of calls and finite capacity, Queudng Systems 19, 215-229 (1995). B.D. Choi and K.H. Rhee, An M/G/l retrial queue with a threshold in the retrial group, Kyungpook Mathematical Journal 35, 469-479 (1996). B.D. Choi and J.W. Kim, Discrete-time Geol, Geoz/G/l retrial queueing systems with two types of calls, Computers Math. Applic. 33 (lo), 79-88 (1997). B.D. Choi, Y.C. Kim and Y.W. Lee, The M/M/c retrial queue with geometric loss and feedback, Computers Math. Applic. 36 (6), 41-52 (1998). B.D. Choi and D.B. Zhu, The Mr,Mz/G/l/K retrial queueing systems with priority, Journal of the Korean Mathematical Society 35, 691-712 (1998). B.D. Choi and Y. Chang, MAPi/MAPz/M/ c with the retrial group of finite capacity and geometric loss, Mathl. Comput. Modelling (this issue). Q.H. Choo and B. Conolly, New results in the theory of repeated orders queueing systems, Journal of Applied Probability 16, 631-640 (1979). B. Conolly, Letter to the editor, Journal of Applied Probability 19, 904-905 (1982).
Accessible Bibliography
3
35. A.G. de Kok, Algorithmic methods for single server systems with repeated attempts, Statistica Neerlandica 38, 23-32 (1984). 36. N. Deul, Stationary conditions for multi-server queueing systems with repeated calls, Journal of Znformation P~~ess~ng and Cy~et~cs 16, 607-613 (1980). 37. N. Deul, The intluence of the perseverance function in queueing systems with repeated calls, Jon~ai of Information Processing and Cybernetics 18, 587-594 (1982). 38. J.E. Diamond and A.S. Alfa, Matrix analytical methods for M/PH/l retrial queues, Stochastic Models Xl, 447-470 (1995). 39. J.E. Diamond and AS. Alfa, The MAP/PH/I retrial queue, Stochastic Models 14, 1151-1177 (1998). 40. A. Dudin and V. Klimenok, Queueing system BMAP/G,fl with repeated calls, Mathl. Comput. Mode6l~ng (this issue). 41. A. Elcan, Optimal customer return rate for an M/M/l queueing system with retrials, P~~b~l~ty in the Engineer&g and Informational Sciences 8, 521-539 (1994). 42. A. Elcan, Asymptotic bounds for an optimal state-dependent retrial rate of the M/M/l queue with returning customers, Mathl. Comput. Modelling (this issue). 43. G.I. Falin, On sufficient conditions for ergodicity of multi-channel queueing systems with repeated calls, Advances in Applied P~~b~~~t~18, 447-448 (1984). of AppZ~~ 44. G.I. Falin, On the waiting time process in a single-line queue with repeated calls, Jou~al Probability 23, 185-192 (1986). 45. G.I. Falin, Multichannel queueing systems with repeated calls under high intensity of repetition, Journal of Information Processing and Cybernetics 23, 3747 (1987). 46. G.I. Falin, On a multiclass batch arrival retrial queue, Advances in Applied Probability 20, 483-487 (1988). 47. G.I. Falin and C!. Fricker, On the virtual waiting time in an M/G/l retrial queue, Journal of Applied P~~bil~ty 28, 446-460 (1991). 48. G.I. Falin, J.R. Artalejo and M. Martin, On the single server retrial queue with priority customers, Queue&g Systems 14, 439-455 (1993). 49. G.I. Falin, M. Martin and J.R. Artalejo, Information theoretic approximations for the M/G/l retrial queue, Acta Znformatica 31, 559-571 (1994). 50. G.I. Falin, Estimation of retrial rate in a retrial queue, Queueing Systems 19, 231-246 (1995). 51. G.I. Falin and J.R. Artalejo, Approximations for multiserver queues with balking/retrial discipline, OR Saturn 17, 239-244 (1995). 52. G.I. Falin and J.R. Artalejo, A finite source retrial queue, European Journal of Operational Research 108, 409424 (1998). 53. G.I. Falin, A multiserver retrial queue with finite number of sources of primary calls, Mathl. Comput. Modelling (this issue). 54. G.I. Falin and A. Gomez-Corral, On a bivariate process arising in the theory of single-server retrial queues, Statistica Neerlandicn (to appear). 55. K. Farahmand, Single line queue with repeated demands, ~ea~ng System 6, 223-228 (1999). 56. K. Farahmand, Single line queue with recurrent repeat demands, QzceueingSystems 22, 425-435 (1996). 57. K. Farahmand and N.H. Smith, Retrial queues with recurrent demand option, Journal of Applied Mathematics and Stochastic Analysis 9, 221-228 (1996). 58. K. Farahmand and N. Cooke, Single retrial queues with service option on arrival, Journal of Applied Mathematics and &&ion Sciences 1, 5-12 (1997). 59. S.W. Fuhrmann and R.B. Cooper, Stochastic decomposition in the M/G/l queue with generalized vacations, ~~t~o~ Research 33, 1117-1129 (1985). 60. D.P. Gaver and J.P. Lehoczky, Gaussian approximations to service problems: A communication system example, Journal of Applied Probability 13, 768-780 (1976). 61. A. GomezXorral and M.F. Ramalhoto, On the stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems, Mathl. Comput. Modelling (this issue). 62. B.S. Greenberg and R.W. Wolff, An upper bound on the performance of queues with returning customers, ~ou~al of Applied P~~b~~ty 24, 466475 (1987). 63. B.S. Greenberg, M/G/l queueing systems with returning customers, Jou~a~ of Applied Probability 26, 152-163
(1989).
S.A. Grishechkin, Multiclass batch arrival retrial queues analyzed as branching processes with immigration, Queueing Systems 11, 395-418 (1992). 65. D.H. Han and Y.W. Lee, MMPP,M/G/l retrial queue with two classes of customers, Communications of the Korean Ma~ernati~~ Society 11, 481493 (1996). 66. T. Hanschke, The M/G/I/l queue with repeated attempts and different types of feedback effects, OR 64.
Spektrum
7, 209-215
(1985).
T. Hanschke, Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts, Journal of Applied Probability 24, 486-494 (1987). 68. T. Hanschke, A matrix continued fraction algorithm for the multi-server repeated order queue, Muthl. Comput. Modelling (this issue). 69. C.M. Harris, K.L. Hoffman and P.B. Saunders, Modeling the IRS telephone taxpayer information system, ~e~t~o~ Research 35, 504-523 (1987).
67.
J. R. ARTALEJO
4
70. R. Hassin and M. Haviv, On optimal and equilibrium retrial rates in a queueing system, Probability in the ~n~~ee~ng and Infa~ati~al Sciences 10, 223-227 (1996). 71. K.L. HofTman and CM. Harris, Estimation of a caller retrial rate for a telephone information system, European Journal of Operational Research 27, 207-214 (1986). 72. J. Keilson, J. Cozzolino and H. Young, A service system with unfillsd requests repeated, Operutions Research 16, 1126-1137 (1968). 73. J. Keilson and L.D. Servi, The matrix M/M/W system: Retrial models and Markov modulated sources, Advances in Appli~ P~~b~I~t~ 25, 453-471 (1993). 74. F.P. Kelly, On autorepeat facilities and telephone network performance, Journal of the Royal Statistical Society 848, 123-132 (1986). 75. Z. Khalil, G.I. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Qveveing Systems 10, 381-402 (1992). 76. Z. Khalil and G.I. F&n, Stochastic in~ualiti~ for M/G/l retrial queues, 0~~~0~s Research Letters 16, 285-290 (1994). 77. Y.C. Kim, On M/M/3/3 retrial queueing system, Hanam Mathematical Journal 17, 141-147 (1995). 78. A. Krishnamoorthy and P.V. Ushakumari, GI/M/l/l queue with finite retrials and finite orbits, Stochastic Analysis and Applications (to appear). 79. V.G. Kulkarni, Letter to the editor, Jou~al of Ap~Zi~ Pro~b~l~t~19, 901-904 (1982). 80. V.G. Kulkarni, On queue@ systems with retrials, Journal of Applied P~~bil~~~ 20, 380-389 (1983). 81. V.G. Kulkarni, A game theoretic model for two types of customers competing for service, Operations Research Letters 2, 119-122 (1983). 82. V.G. Kulkarni, Expected waiting times in a multiclsss batch arrival retrial queue, Jownal of Applied P~babi~~t~23, 144-154 (1986). 83. V.G. Kulkarni and S.P. Sethi, Deterministic retrial times are optimal in queues with forbidden states, fnfor 27, 374-386 (1989). 84. V.G. Kulkarni and B.D. Choi, Retrial queues with server subject to breakdowns and repairs, Queueing Systems 7, 191-208 (1990). 85. C. Langaris and E. Moutzoukis, A retrial queue with structured batch arrivals, priorities and server vacations, ~eue~~g Systems 20, 341-368 (1995). 86. C. Langaris, A polfing model with retrial customers, Journal of the Operations Research Society of Japan 87. 88.
40, 489-508 (1997). C. Langaris and E. Moutzoukis, A batch arrival reader-writerqueue with retrial writers, Stochastic Models 13, 523-545 (1997). C. Langaris, Gated polling models with customers in orbit, Muthl. Compnt. quelling (this issue).
89. H. Li and T. Yang, A single-serverretrial queue with server vacations and a finite number of input sources, European
Journal
of Operational
Research 85, 149-160
(1995).
H. Li and T. Yang, Gee/G/l discrete-time retrial queue with Bernoulli schedule, European Journal of Opemtional Research 111, 629-649 (1998). 91. H. Li and T. Yang, The steady-state queue size distribution of discrete-time PH/Geo/l retrial queue, h&a&l. Comput. quelling (this issue). 92. H.M. Liang and V.G. Kulkarni, Stability condition for a single-server retrial queue, Advances in Applied 90.
Probability 25, 690-701 93.
(1993).
H.M. Liang and V.G. Kulkarni, Monotonicity properties of single-server retrial queues, Stochastic Models 9, 373-400
(1993).
H.M. Liang, Service station factors in monotonicity of retrial queues, Gaul. Comput. quelling (this issue), 95. R.E. Lillo, A G/M/l-queue with exponential retrial, Top 4, W-120 (1996). 96. M. Martin and J.R. Artalejo, Analysis of an M/G/1 queue with two types of impatient units, Advances in 94.
Applied Probability 27, 840-861 97.
98. 99.
100. 101. 102.
103. 104. 105.
(1995).
M. Martin and A. Gomez-Corral, On the M/G/l retrial queueing system with linear control policy, Top 3, 285-305 ( 1995). E. Moutzoukis and C. Langaris, Non-pr~mptive priorities and vacations in a multiclass retrial queueing system, Stochastic Models 12,455-472 (1996). M.F. Neuts and M.F. Ramalhoto, A service model in which the server is required to search for customers, Journal of Applied Probability 21, 157-166 (1984). M.F. Neuts and B.M. Rae, Numerical investigation of a multiserver retrial model, QuezaeingSystems 7, 169-190 (1990). C.E.M. Pearce, On the problem of reattempted calls in teletra&, Stochastic Models 3, 393-407 (1987). C.E.M. Pearce, Extended continued fractions, recurrence relations and two dimensional Markov processes, Advances in Applied Probability 21, 357-375 (1989). B. Pourbabai, Analysis of a G/M/K/O queueing loss system with heterogeneous servers and retrials, International Journal of System Science 18, 985-992 (1987). B. Pourbabai, Asymptotic analysis of G/G/K queueing-l~sy~em with retrials and heterogeneous servers, International Journal of System Science 19, 1047-1052 (1988). B. Pourbabai, A random access telecommunication system, Journal of Information Processing and Cybernetics 24, 613-625 (1988).
Accessible
107.
110. 111. 112. 113. 114. 115. 116. 117.
118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128.
Bibliography
B. Pourbabai, A finite capacity telecommunication system with repeated calls, Journal of Information Processing and Cybernetics 25, 457-467 (1989). B. Pourbabai, Tandem behaviour of a telecommunication system with repeated calls: A Markovian case with buffers, JoumaI of the Operational Research Society 40, 671-680 (1989). B. Pourbabai, A note on a D/G/K loss system with retrials, Journal of Applied Probability 27, 385-392 (1990). B. Pourbabai, Tandem behavior of a telecommunication system with finite buffers and repeated calls, Queueing Systems 6, 89-108 (1990). B. Pourbabai, Tandem behavior of a telecommunication system with repeated calls: II, A general case without buffers, European Journal of Operational Research 65, 247-258 (1993). M.F. Ramalhoto and A. Gomez-Corral, Some decomposition formulae for M/M/r/r+d queues with constant retrial rate, Stochastic Models 14, 123-145 (1998). A. Hodrigo, M. Vazquez and G.I. Falin, A new Markovian description of the M/G/l retrial queue, European Journal of Operational Research 104, 231-240 (1998). A. Rodrigo and M. Vazquez, Large sample inference in retrial queues, Mathl. Comput. Modelling (this issue). F.M. Spieksma and R.L. Tweedie, Strengthening ergodicity to geometric ergodicity for Markov chains, Stochastic Models 10, 45-74 (1994). S.N. Stepanov, Probabilistic characteristics of an incompletely accessible multi-phase service system with several types of repeated call, Prublems of Conlrul and Information Theory 10, 1-12 (1981). S.N. Stepanov, Asymptotic formulae and estimations for probability characteristics of full-available group with absolutely persistent subscribers, Problems of Control and Information Theory 12, 361-369 (1983). S.N. Stepanov, Probabilistic characteristics of an incompletely accessible service system with repeated calls for arbitrary values of subscriber persistent function, Problems of Control and Information Theory 13, 69-78 (1984). S.N. Stepanov, Numerical calculation accuracy of communication models with repeated calls, Problems of Control and Information Theory 13, 371-381 (1984). S.N. Stepanov and 1.1. Tsitovich, The model of a full-available group with repeated calls and waiting positions in the case of extreme load, Problems of Control and Injormation Theory 14, 25-32 (1985). S.N. Stepanov, Generalized model with repeated calls in case of extreme load, Queueing Systems 27, 131-151 (1997). S.N. Stepanov, Markov models with retrials: The calculation of stationary performance measures based on the concept of truncation, Mathl. Comput. Modelling (this issue). G.K. Takahara, Fixed point approximations for retrial networks, Probability in the Engineering and Injormational Sciences 10, 243-259 (1996). M. Vazquez, A retrial model in a nonstationary regime, Top 4, 121-133 (1996). T. Yang, M.J.M. Posner and J.G.C. Templeton, The M/G/l retrial queue with nonpersistent customers, Queueing Systems 7, 209-218 (1990). T. Yang, M.J.M. Posner and J.G.C. Templeton, The &/M/S/ m retrial queue: A computational approach, ORSA Journal on Computing 4, 182-191 (1992). T. Yang and H. Li, The M/G/l retrial queue with the server subject to starting failures, Queueing Systems 16, 83-96 (1994). T. Yang, M.J.M. Posner, J.G.C. Templeton and H. Li, An approximation method for the M/G/l retrial queue with general retrial times, European Journal of Operational Research 78, 552-562 (1994). T. Yang and H. Li, On the steady-state queue size distribution of the discretetime G-/G/l queue with repeated customers, Queueing Systems 21, 199-215 (1995).
TELECOMMUNICATION 1. 2. 3. 4. 5. 6. 7. 8. 9.
5
JOURNALS
L.T.M. Berry, A repeated calls model encompassing non-Poisson traffic streams in alternative routing networks, Australian Telecommunication Research 21, 21-28 (1987). C. Clos, An aspect of the dialing behavior of subscribers and its effect on the trunk plant, The Bell System Technical Journal 27, 424-445 (1948). J.W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls, Philips Telecommunication Review 18, 49-100 (1957). F.P. Duffy and R.A. Mercer, A study of network performance and customer behavior during direct-distancedialing call attempts in the USA, The Bell System Technical Journal 57, l-33 (1978). A. Elldin, Approach to the theoretical description of repeated call attempts, Ericsson Technics 23, 345-407 (1967). A. Elldin, ‘&a% engineering in developing countries. Some observations from the ESCAP region, Tefewmmunicntion Journal 44, 427-436 (1977). A.A. Fredericks and G.A. Reisner, Approximations to stochastic service systems, with an application to a retrial model, The Bell System Technical Journal 58, 557-576 (1979). E.N. Gilbert, Retrials and balks, IEEE Tbnnsactions on Information Theory 34, 1502-1508 (1988). G. Gosztony, Repeated call attempts and their effect on traffic engineering, Budavoz Telecommunication Review. No. 2, 16-26 (1976).
J. R. ARTALEJO
6 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
G. Gosztony, Comparison of calculated and simulated results for trunk groups with repeated attempts, Budavox Telecommunication Review, No. 1, 1-18 (1977). G. Gosztony, K. Rahko and R. Chapuis, The grade of service in the world-wide telephone network, Part I, Telecommunication Journal 46, 556-565 (1979). N. Grier, W.A. Massey, T. McKay and W. Whitt, The time-dependent Erlang loss model with retrials, Telecommunication Systems 7, 253-265 (1997). G. Honi, Some macro-models for discussing repeated call attempts, Budavox Telecommunication Review, No. 2, 21-39 (1975). W.B. Iversen, Analysis of real teletral%c processes based on computerized measurements, Ericsson Technics 29, 3-64 (1973). G.K. Janssens, The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network, IEEE lPransactions on Communications 45, 360-364 (1997). K.S. Liu, Direct distance dialing: Call completion and customer retrial behavior, The Bell System Technical Journal 59, 295-311 (1980). S.J. Lupker, G.J. Fleet and B.R. Shelton, Caller’s perceptions of post-dialing delays: The effects of a new signalling technology, Behaviour and Information Technology 7, 263-274 (1988). A. Myskja, A recording and processing system for accounting and traffic analysis on a large PABX, IEEE l%ansactions on Communication Technology 19, 692-699 (1971). A. Myskja and F.A. Aagesen, On the interaction between subscribers and a telephone system, Telektronikk 3, 271-282 (1977). A. Myskja and 0.0. Walmann, An investigation of telephone-user habits by means of computer techniques, IEEE tinsactions on Communications 21, 663-671 (1973). L. Nader, The effects of traffic overloads in automatic telephone networks, Budavox Telecommunication Review, No. 1, 2-17 (1988). D.J. Songhurst, Subscriber repeat attempts, congestion and the quality of service: A study baaed on network simulation, British Telecommunication Technology Journal 2, 47-55 (1984). R.I. Wilkinson, Theories for toll traflic engineering in the USA, The Bell System Technical Journal 35, 421-514 (1956). T.Yokoi, End-to-end blocking probability in telecommunication networks and repeated call attempts, Review of the Electrical Communications Laboratories 36, 23-28 (1988).
PERGAMON
www.elsevier.nl/locate/mcm
Accessible Bibliography on Retrial Queues J. R. ARTALEJO Departamento de Estadistica e I.O., Facultad de Matematicas Universidad Complutense de Madrid, 28040 Madrid, Spain j esus_artale johat . ucm.es Research
papers on retrial
queueing
systems
and their applications
have been published
in a va-
riety of mathematical and telecommunication journals, proceedings of international conferences, Ph.D. theses, and working papers of research institutions. Recently, Falin and Templeton published the first monograph
on retrial
queues, which gives a systematic
account
of the fundamental
methods and results on this topic. Some other books on queueing theory and stochastic systems, and several surveys also provide useful information about the existing results and open problems. It should also be noted that papers on retrial queues are published in many languages (we specially mention the Russian literature). The access to an English translation is often difficult or indeed impossible. Based on these observations, the author thought it might perhaps be useful to provide a bibliography including references easily accessible for the whole queueing community. To that end, the author in English. Of course, in translated
papers,
decided to include there is a certain
languages
other
than
only books and papers published in journals written subjectivity in this criterion, so readers interested English,
referred to the monograph by Falin and Templeton. The author is indebted to the people who helped
theses,
and proceedings
him by bringing
of conferences
are
new works of reference.
BOOKS 1. G.I. Falin and J.G.C. Templeton, Retrial Queues, Chapman and Hall, (1997). 2. V.G. Kulkami, Modeling and Analysis of Stochastic Systems, Chapman and Hall. (1995). 3. J. Riordan, Stochastic Service Systems, Wiley, (1962). 4. R. Syski, Introduction to Congestion Theory in Telephone Systems, North-Holland, (1986). 5. R.W. Wolff, Stochastic Modeling and the Theory of Queues, Prentince-Hall, (1989).
SURVEYS 1. J.R. Artalejo, Retrial queues with a finite number of sources, Journal of the Korean Mathematrcul Society 35, 503-525 (1998). 2. B.D. Choi and Y. Chang, Single server retrial queues with priority calls, Mathl. Cornput. Modelling (this issue). 3. G.I. Falin, Singleline repeated orders queueing systems, Optimization 17, 649-667 (1986). 4. G.I. Falin, A survey of retrial queues, Queveing Systems 7. 127-167 (1990). 5. V.G. Kulkami and H.M. Liang, Retrial queues revisited, In Rontiers in Queueing, (Edited by J.H. Dshalalow), pp. 19-34, CRC Press, (1997). 6. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2, 201-233 (1987); Correction, Queueing Systems 4, 94 (1989).
08957177/99/% - see front matter. P11:s0895-7177(99)00128-4
@ 1999 EIsevier Science Ltd. All rights reserved.
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by &+TE)c
2
J. R. ARTALEJO
MATHEMATICAL
JOURNALS
1. A. Aissani, Unreliable queueing with repeated orders, Microelectronics and Reliability 33, 2093-2106 (1993). 2. A. Aissani, A retrial queue with redundancy and unreliable server, Queueing Systems 17, 431-449 (1994). 3. A. Aissani and J.R. Artalejo, On the single server retrial queue subject to breakdowns, Queueing Systems 30, 309-321 (1998). 4. E. Altman and A.A. Borovkov, On the stability of retrial queues, Queueing Systems 26, 343-363 (1997). 5. V.V. Anisimov, Averaging methods for transient regimes in overloading retrial queueing systems, Mathl. Cornput. Modelling (this issue). 6. J.R. Artalejo, Explicit formulae for the characteristics of the M/Hz/l retrial queue, Jownal of the Operational Research Society 44, 309-313 (1993). 7. J.R. Artalejo, New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandicu 48, 23-36 (1994). 8. J.R. Artalejo and G.I. Falin, Stochastic decomposition for retrial queues, Top 2, 329-342 (1994). 9. J.R. Artalejo, A queueing system with returning customers and waiting line, Operations Research Letters 17, 191-199 (1995). 10. J.R. ArtaIejo and A. Gomez-Corral, Information theoretic analysis for queueing systems with quasi-random input, Mathl. Comput. Modelling 22 (3), 65-76 (1995). 11. J.R. Artalejo, Stationary analysis of the characteristics of the M/M/2 queue with constant repeated attempts, Opsearch 33, 83-95 (1996). 12. J.R. ArtaIejo and G.I. Falin, On the orbit characteristics of the M/G/l retrial queue, Naval Research Logistics 43, 1147-l 161 (1996). 13. J.R. Artalejo and A. Gomez-Corral, Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue, Journal of Applied Mathematics and Stochastic Analysis 9, 171-183 (1996). 14. J.R. Artalejo, Analysis of an M/G/l queue with constant repeated attempts and server vacations, Computers and Operations Research 24, 493-504 (1997). 15. J.R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated requests, Journal of Applied Probability 34, 223-233 (1997). 16. J.R. Artalejo and A. Gomez-Corral, Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals, OR Spektrum 20, 5-14 (1998). 17. J.R. Artalejo and A. Gomez-Corral, Analysis of a stochastic clearing system with repeated attempts, Stochastic Models 14, 623-645 (1998). 18. J.R. Artalejo and A. Gomez-Corral, On a single server queue with negative arrivals and request repeated, Journal of Applied Probability 38 (1999). 19. J.R. Artalejo and A. Gomez-Corral, Performance analysis of a single-server queue with repeated attempts, Mathl. Comput. Modelling (this issue). 20. J.R. ArtaIejo and A. Gomez-Corral. Computation of the limiting distribution in queueing systems with repeated attempts and disasters, RO-Recherche OpemtionnaIle/Opemtions Research (to appear). 21. P.P. Bocharov, 0.1. Pavlova and D.A. Puzikova, M/G/l/r retrial queueing systems with priority of primary customers, Mathl. Comput. Modelling (this issue). 22. B.D. Choi and K.K. Park, The M/G/l retrial queue with Bernoulli schedule, Queueing Systems 7, 219-227 (1990). 23. B.D. Choi, Y.W. Shin and W.C. Ahn. Retrial queues with collision arising from unslotted CSMA/CD protocol, Queueing Systems 11, 335-356 (1992). 24. B.D. Choi, D.H. Han and G.1. Falin, On the virtual waiting time for an M/G/l retrial queue with two types of calls, Journal of Applied Mathematics and Stochastic Analysis 6, 1 l-23 (1993). 25. B.D. Choi, K.K. Park and C.E.M. Pearce, An M/M/l retrial queue with control policy and general retrial times, Queueing Systems 14, 275-292 (1993). 26. 27. 28. 29. 30. 31. 32. 33. 34.
B.D. Choi, K.H. Rhee and K.K. Park, The ,M/G/l retrial queue with retrial rate control policy, Probability in the Engineering and Informational Sciences 7, 2s46 (1993). B.D. Choi, K.B. Choi and Y.W. Lee, M/G/l retrial queueing systems with two types of calls and finite capacity, Queudng Systems 19, 215-229 (1995). B.D. Choi and K.H. Rhee, An M/G/l retrial queue with a threshold in the retrial group, Kyungpook Mathematical Journal 35, 469-479 (1996). B.D. Choi and J.W. Kim, Discrete-time Geol, Geoz/G/l retrial queueing systems with two types of calls, Computers Math. Applic. 33 (lo), 79-88 (1997). B.D. Choi, Y.C. Kim and Y.W. Lee, The M/M/c retrial queue with geometric loss and feedback, Computers Math. Applic. 36 (6), 41-52 (1998). B.D. Choi and D.B. Zhu, The Mr,Mz/G/l/K retrial queueing systems with priority, Journal of the Korean Mathematical Society 35, 691-712 (1998). B.D. Choi and Y. Chang, MAPi/MAPz/M/ c with the retrial group of finite capacity and geometric loss, Mathl. Comput. Modelling (this issue). Q.H. Choo and B. Conolly, New results in the theory of repeated orders queueing systems, Journal of Applied Probability 16, 631-640 (1979). B. Conolly, Letter to the editor, Journal of Applied Probability 19, 904-905 (1982).
Accessible Bibliography
3
35. A.G. de Kok, Algorithmic methods for single server systems with repeated attempts, Statistica Neerlandica 38, 23-32 (1984). 36. N. Deul, Stationary conditions for multi-server queueing systems with repeated calls, Journal of Znformation P~~ess~ng and Cy~et~cs 16, 607-613 (1980). 37. N. Deul, The intluence of the perseverance function in queueing systems with repeated calls, Jon~ai of Information Processing and Cybernetics 18, 587-594 (1982). 38. J.E. Diamond and A.S. Alfa, Matrix analytical methods for M/PH/l retrial queues, Stochastic Models Xl, 447-470 (1995). 39. J.E. Diamond and AS. Alfa, The MAP/PH/I retrial queue, Stochastic Models 14, 1151-1177 (1998). 40. A. Dudin and V. Klimenok, Queueing system BMAP/G,fl with repeated calls, Mathl. Comput. Mode6l~ng (this issue). 41. A. Elcan, Optimal customer return rate for an M/M/l queueing system with retrials, P~~b~l~ty in the Engineer&g and Informational Sciences 8, 521-539 (1994). 42. A. Elcan, Asymptotic bounds for an optimal state-dependent retrial rate of the M/M/l queue with returning customers, Mathl. Comput. Modelling (this issue). 43. G.I. Falin, On sufficient conditions for ergodicity of multi-channel queueing systems with repeated calls, Advances in Applied P~~b~~~t~18, 447-448 (1984). of AppZ~~ 44. G.I. Falin, On the waiting time process in a single-line queue with repeated calls, Jou~al Probability 23, 185-192 (1986). 45. G.I. Falin, Multichannel queueing systems with repeated calls under high intensity of repetition, Journal of Information Processing and Cybernetics 23, 3747 (1987). 46. G.I. Falin, On a multiclass batch arrival retrial queue, Advances in Applied Probability 20, 483-487 (1988). 47. G.I. Falin and C!. Fricker, On the virtual waiting time in an M/G/l retrial queue, Journal of Applied P~~bil~ty 28, 446-460 (1991). 48. G.I. Falin, J.R. Artalejo and M. Martin, On the single server retrial queue with priority customers, Queue&g Systems 14, 439-455 (1993). 49. G.I. Falin, M. Martin and J.R. Artalejo, Information theoretic approximations for the M/G/l retrial queue, Acta Znformatica 31, 559-571 (1994). 50. G.I. Falin, Estimation of retrial rate in a retrial queue, Queueing Systems 19, 231-246 (1995). 51. G.I. Falin and J.R. Artalejo, Approximations for multiserver queues with balking/retrial discipline, OR Saturn 17, 239-244 (1995). 52. G.I. Falin and J.R. Artalejo, A finite source retrial queue, European Journal of Operational Research 108, 409424 (1998). 53. G.I. Falin, A multiserver retrial queue with finite number of sources of primary calls, Mathl. Comput. Modelling (this issue). 54. G.I. Falin and A. Gomez-Corral, On a bivariate process arising in the theory of single-server retrial queues, Statistica Neerlandicn (to appear). 55. K. Farahmand, Single line queue with repeated demands, ~ea~ng System 6, 223-228 (1999). 56. K. Farahmand, Single line queue with recurrent repeat demands, QzceueingSystems 22, 425-435 (1996). 57. K. Farahmand and N.H. Smith, Retrial queues with recurrent demand option, Journal of Applied Mathematics and Stochastic Analysis 9, 221-228 (1996). 58. K. Farahmand and N. Cooke, Single retrial queues with service option on arrival, Journal of Applied Mathematics and &&ion Sciences 1, 5-12 (1997). 59. S.W. Fuhrmann and R.B. Cooper, Stochastic decomposition in the M/G/l queue with generalized vacations, ~~t~o~ Research 33, 1117-1129 (1985). 60. D.P. Gaver and J.P. Lehoczky, Gaussian approximations to service problems: A communication system example, Journal of Applied Probability 13, 768-780 (1976). 61. A. GomezXorral and M.F. Ramalhoto, On the stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems, Mathl. Comput. Modelling (this issue). 62. B.S. Greenberg and R.W. Wolff, An upper bound on the performance of queues with returning customers, ~ou~al of Applied P~~b~~ty 24, 466475 (1987). 63. B.S. Greenberg, M/G/l queueing systems with returning customers, Jou~a~ of Applied Probability 26, 152-163
(1989).
S.A. Grishechkin, Multiclass batch arrival retrial queues analyzed as branching processes with immigration, Queueing Systems 11, 395-418 (1992). 65. D.H. Han and Y.W. Lee, MMPP,M/G/l retrial queue with two classes of customers, Communications of the Korean Ma~ernati~~ Society 11, 481493 (1996). 66. T. Hanschke, The M/G/I/l queue with repeated attempts and different types of feedback effects, OR 64.
Spektrum
7, 209-215
(1985).
T. Hanschke, Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts, Journal of Applied Probability 24, 486-494 (1987). 68. T. Hanschke, A matrix continued fraction algorithm for the multi-server repeated order queue, Muthl. Comput. Modelling (this issue). 69. C.M. Harris, K.L. Hoffman and P.B. Saunders, Modeling the IRS telephone taxpayer information system, ~e~t~o~ Research 35, 504-523 (1987).
67.
J. R. ARTALEJO
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70. R. Hassin and M. Haviv, On optimal and equilibrium retrial rates in a queueing system, Probability in the ~n~~ee~ng and Infa~ati~al Sciences 10, 223-227 (1996). 71. K.L. HofTman and CM. Harris, Estimation of a caller retrial rate for a telephone information system, European Journal of Operational Research 27, 207-214 (1986). 72. J. Keilson, J. Cozzolino and H. Young, A service system with unfillsd requests repeated, Operutions Research 16, 1126-1137 (1968). 73. J. Keilson and L.D. Servi, The matrix M/M/W system: Retrial models and Markov modulated sources, Advances in Appli~ P~~b~I~t~ 25, 453-471 (1993). 74. F.P. Kelly, On autorepeat facilities and telephone network performance, Journal of the Royal Statistical Society 848, 123-132 (1986). 75. Z. Khalil, G.I. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Qveveing Systems 10, 381-402 (1992). 76. Z. Khalil and G.I. F&n, Stochastic in~ualiti~ for M/G/l retrial queues, 0~~~0~s Research Letters 16, 285-290 (1994). 77. Y.C. Kim, On M/M/3/3 retrial queueing system, Hanam Mathematical Journal 17, 141-147 (1995). 78. A. Krishnamoorthy and P.V. Ushakumari, GI/M/l/l queue with finite retrials and finite orbits, Stochastic Analysis and Applications (to appear). 79. V.G. Kulkarni, Letter to the editor, Jou~al of Ap~Zi~ Pro~b~l~t~19, 901-904 (1982). 80. V.G. Kulkarni, On queue@ systems with retrials, Journal of Applied P~~bil~~~ 20, 380-389 (1983). 81. V.G. Kulkarni, A game theoretic model for two types of customers competing for service, Operations Research Letters 2, 119-122 (1983). 82. V.G. Kulkarni, Expected waiting times in a multiclsss batch arrival retrial queue, Jownal of Applied P~babi~~t~23, 144-154 (1986). 83. V.G. Kulkarni and S.P. Sethi, Deterministic retrial times are optimal in queues with forbidden states, fnfor 27, 374-386 (1989). 84. V.G. Kulkarni and B.D. Choi, Retrial queues with server subject to breakdowns and repairs, Queueing Systems 7, 191-208 (1990). 85. C. Langaris and E. Moutzoukis, A retrial queue with structured batch arrivals, priorities and server vacations, ~eue~~g Systems 20, 341-368 (1995). 86. C. Langaris, A polfing model with retrial customers, Journal of the Operations Research Society of Japan 87. 88.
40, 489-508 (1997). C. Langaris and E. Moutzoukis, A batch arrival reader-writerqueue with retrial writers, Stochastic Models 13, 523-545 (1997). C. Langaris, Gated polling models with customers in orbit, Muthl. Compnt. quelling (this issue).
89. H. Li and T. Yang, A single-serverretrial queue with server vacations and a finite number of input sources, European
Journal
of Operational
Research 85, 149-160
(1995).
H. Li and T. Yang, Gee/G/l discrete-time retrial queue with Bernoulli schedule, European Journal of Opemtional Research 111, 629-649 (1998). 91. H. Li and T. Yang, The steady-state queue size distribution of discrete-time PH/Geo/l retrial queue, h&a&l. Comput. quelling (this issue). 92. H.M. Liang and V.G. Kulkarni, Stability condition for a single-server retrial queue, Advances in Applied 90.
Probability 25, 690-701 93.
(1993).
H.M. Liang and V.G. Kulkarni, Monotonicity properties of single-server retrial queues, Stochastic Models 9, 373-400
(1993).
H.M. Liang, Service station factors in monotonicity of retrial queues, Gaul. Comput. quelling (this issue), 95. R.E. Lillo, A G/M/l-queue with exponential retrial, Top 4, W-120 (1996). 96. M. Martin and J.R. Artalejo, Analysis of an M/G/1 queue with two types of impatient units, Advances in 94.
Applied Probability 27, 840-861 97.
98. 99.
100. 101. 102.
103. 104. 105.
(1995).
M. Martin and A. Gomez-Corral, On the M/G/l retrial queueing system with linear control policy, Top 3, 285-305 ( 1995). E. Moutzoukis and C. Langaris, Non-pr~mptive priorities and vacations in a multiclass retrial queueing system, Stochastic Models 12,455-472 (1996). M.F. Neuts and M.F. Ramalhoto, A service model in which the server is required to search for customers, Journal of Applied Probability 21, 157-166 (1984). M.F. Neuts and B.M. Rae, Numerical investigation of a multiserver retrial model, QuezaeingSystems 7, 169-190 (1990). C.E.M. Pearce, On the problem of reattempted calls in teletra&, Stochastic Models 3, 393-407 (1987). C.E.M. Pearce, Extended continued fractions, recurrence relations and two dimensional Markov processes, Advances in Applied Probability 21, 357-375 (1989). B. Pourbabai, Analysis of a G/M/K/O queueing loss system with heterogeneous servers and retrials, International Journal of System Science 18, 985-992 (1987). B. Pourbabai, Asymptotic analysis of G/G/K queueing-l~sy~em with retrials and heterogeneous servers, International Journal of System Science 19, 1047-1052 (1988). B. Pourbabai, A random access telecommunication system, Journal of Information Processing and Cybernetics 24, 613-625 (1988).
Accessible
107.
110. 111. 112. 113. 114. 115. 116. 117.
118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128.
Bibliography
B. Pourbabai, A finite capacity telecommunication system with repeated calls, Journal of Information Processing and Cybernetics 25, 457-467 (1989). B. Pourbabai, Tandem behaviour of a telecommunication system with repeated calls: A Markovian case with buffers, JoumaI of the Operational Research Society 40, 671-680 (1989). B. Pourbabai, A note on a D/G/K loss system with retrials, Journal of Applied Probability 27, 385-392 (1990). B. Pourbabai, Tandem behavior of a telecommunication system with finite buffers and repeated calls, Queueing Systems 6, 89-108 (1990). B. Pourbabai, Tandem behavior of a telecommunication system with repeated calls: II, A general case without buffers, European Journal of Operational Research 65, 247-258 (1993). M.F. Ramalhoto and A. Gomez-Corral, Some decomposition formulae for M/M/r/r+d queues with constant retrial rate, Stochastic Models 14, 123-145 (1998). A. Hodrigo, M. Vazquez and G.I. Falin, A new Markovian description of the M/G/l retrial queue, European Journal of Operational Research 104, 231-240 (1998). A. Rodrigo and M. Vazquez, Large sample inference in retrial queues, Mathl. Comput. Modelling (this issue). F.M. Spieksma and R.L. Tweedie, Strengthening ergodicity to geometric ergodicity for Markov chains, Stochastic Models 10, 45-74 (1994). S.N. Stepanov, Probabilistic characteristics of an incompletely accessible multi-phase service system with several types of repeated call, Prublems of Conlrul and Information Theory 10, 1-12 (1981). S.N. Stepanov, Asymptotic formulae and estimations for probability characteristics of full-available group with absolutely persistent subscribers, Problems of Control and Information Theory 12, 361-369 (1983). S.N. Stepanov, Probabilistic characteristics of an incompletely accessible service system with repeated calls for arbitrary values of subscriber persistent function, Problems of Control and Information Theory 13, 69-78 (1984). S.N. Stepanov, Numerical calculation accuracy of communication models with repeated calls, Problems of Control and Information Theory 13, 371-381 (1984). S.N. Stepanov and 1.1. Tsitovich, The model of a full-available group with repeated calls and waiting positions in the case of extreme load, Problems of Control and Injormation Theory 14, 25-32 (1985). S.N. Stepanov, Generalized model with repeated calls in case of extreme load, Queueing Systems 27, 131-151 (1997). S.N. Stepanov, Markov models with retrials: The calculation of stationary performance measures based on the concept of truncation, Mathl. Comput. Modelling (this issue). G.K. Takahara, Fixed point approximations for retrial networks, Probability in the Engineering and Injormational Sciences 10, 243-259 (1996). M. Vazquez, A retrial model in a nonstationary regime, Top 4, 121-133 (1996). T. Yang, M.J.M. Posner and J.G.C. Templeton, The M/G/l retrial queue with nonpersistent customers, Queueing Systems 7, 209-218 (1990). T. Yang, M.J.M. Posner and J.G.C. Templeton, The &/M/S/ m retrial queue: A computational approach, ORSA Journal on Computing 4, 182-191 (1992). T. Yang and H. Li, The M/G/l retrial queue with the server subject to starting failures, Queueing Systems 16, 83-96 (1994). T. Yang, M.J.M. Posner, J.G.C. Templeton and H. Li, An approximation method for the M/G/l retrial queue with general retrial times, European Journal of Operational Research 78, 552-562 (1994). T. Yang and H. Li, On the steady-state queue size distribution of the discretetime G-/G/l queue with repeated customers, Queueing Systems 21, 199-215 (1995).
TELECOMMUNICATION 1. 2. 3. 4. 5. 6. 7. 8. 9.
5
JOURNALS
L.T.M. Berry, A repeated calls model encompassing non-Poisson traffic streams in alternative routing networks, Australian Telecommunication Research 21, 21-28 (1987). C. Clos, An aspect of the dialing behavior of subscribers and its effect on the trunk plant, The Bell System Technical Journal 27, 424-445 (1948). J.W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls, Philips Telecommunication Review 18, 49-100 (1957). F.P. Duffy and R.A. Mercer, A study of network performance and customer behavior during direct-distancedialing call attempts in the USA, The Bell System Technical Journal 57, l-33 (1978). A. Elldin, Approach to the theoretical description of repeated call attempts, Ericsson Technics 23, 345-407 (1967). A. Elldin, ‘&a% engineering in developing countries. Some observations from the ESCAP region, Tefewmmunicntion Journal 44, 427-436 (1977). A.A. Fredericks and G.A. Reisner, Approximations to stochastic service systems, with an application to a retrial model, The Bell System Technical Journal 58, 557-576 (1979). E.N. Gilbert, Retrials and balks, IEEE Tbnnsactions on Information Theory 34, 1502-1508 (1988). G. Gosztony, Repeated call attempts and their effect on traffic engineering, Budavoz Telecommunication Review. No. 2, 16-26 (1976).
J. R. ARTALEJO
6 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
G. Gosztony, Comparison of calculated and simulated results for trunk groups with repeated attempts, Budavox Telecommunication Review, No. 1, 1-18 (1977). G. Gosztony, K. Rahko and R. Chapuis, The grade of service in the world-wide telephone network, Part I, Telecommunication Journal 46, 556-565 (1979). N. Grier, W.A. Massey, T. McKay and W. Whitt, The time-dependent Erlang loss model with retrials, Telecommunication Systems 7, 253-265 (1997). G. Honi, Some macro-models for discussing repeated call attempts, Budavox Telecommunication Review, No. 2, 21-39 (1975). W.B. Iversen, Analysis of real teletral%c processes based on computerized measurements, Ericsson Technics 29, 3-64 (1973). G.K. Janssens, The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network, IEEE lPransactions on Communications 45, 360-364 (1997). K.S. Liu, Direct distance dialing: Call completion and customer retrial behavior, The Bell System Technical Journal 59, 295-311 (1980). S.J. Lupker, G.J. Fleet and B.R. Shelton, Caller’s perceptions of post-dialing delays: The effects of a new signalling technology, Behaviour and Information Technology 7, 263-274 (1988). A. Myskja, A recording and processing system for accounting and traffic analysis on a large PABX, IEEE l%ansactions on Communication Technology 19, 692-699 (1971). A. Myskja and F.A. Aagesen, On the interaction between subscribers and a telephone system, Telektronikk 3, 271-282 (1977). A. Myskja and 0.0. Walmann, An investigation of telephone-user habits by means of computer techniques, IEEE tinsactions on Communications 21, 663-671 (1973). L. Nader, The effects of traffic overloads in automatic telephone networks, Budavox Telecommunication Review, No. 1, 2-17 (1988). D.J. Songhurst, Subscriber repeat attempts, congestion and the quality of service: A study baaed on network simulation, British Telecommunication Technology Journal 2, 47-55 (1984). R.I. Wilkinson, Theories for toll traflic engineering in the USA, The Bell System Technical Journal 35, 421-514 (1956). T.Yokoi, End-to-end blocking probability in telecommunication networks and repeated call attempts, Review of the Electrical Communications Laboratories 36, 23-28 (1988).