×
Di Crescenzo, Antonio; Giorno, Virginia; Krishna Kumar, Balasubramanian; Nobile, Amelia G.

A time-non-homogeneous double-ended queue with failures and repairs and its continuous approximation. (English) Zbl 1524.60230

Mathematics 6, No. 5, Paper No. 81, 23 p. (2018).

Cited in 14 Documents

MSC:

60K25 Queueing theory (aspects of probability theory)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

double-ended queues; time-non-homogeneous birth-death processes; catastrophes; repairs; transient probabilities; periodic intensity functions; time-non-homogeneous jump-diffusion processes; transition densities; first-passage-time
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Kashyap, B.R.K.; A double-ended queueing system with limited waiting space; Proc. Natl. Inst. Sci. India A: 1965; Volume 31 ,559-570. · Zbl 0149.13602
[2] Kashyap, B.R.K.; The double-ended queue with bulk service and limited waiting space; Oper. Res.: 1966; Volume 14 ,822-834. · Zbl 0147.16602
[3] Sharma, O.P.; Nair, N.S.K.; Transient behaviour of a double ended Markovian queue; Stoch. Anal. Appl.: 1991; Volume 9 ,71-83. · Zbl 0721.60116
[4] Tarabia, A.M.K.; On the transient behaviour of a double ended Markovian queue; J. Combin. Inf. Syst. Sci.: 2001; Volume 26 ,125-134. · Zbl 1219.60080
[5] Conolly, B.W.; Parthasarathy, P.R.; Selvaraju, N.; Doubled-ended queues with impatience; Comput. Oper. Res.: 2002; Volume 29 ,2053-2072. · Zbl 1010.90011
[6] Elalouf, A.; Perlman, Y.; Yechiali, U.; A double-ended queueing model for dynamic allocation of live organs based on a best-fit criterion; Appl. Math. Model.: 2018; . · Zbl 1480.90101
[7] Takahashi, M.; Ōsawa, H.; Fujisawa, T.; On a synchronization queue with two finite buffers; Queueing Syst.: 2000; Volume 36 ,107-123. · Zbl 0966.60093
[8] Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Constructing transient birth-death processes by means of suitable transformations; Appl. Math. Comput.: 2016; Volume 281 ,152-171. · Zbl 1410.60087
[9] Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Analysis of reflected diffusions via an exponential time-based transformation; J. Stat. Phys.: 2016; Volume 163 ,1425-1453. · Zbl 1346.82024
[10] Di Crescenzo, A.; Giorno, V.; Krishna Kumar, B.; Nobile, A.G.; A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation; Methodol. Comput. Appl. Probab.: 2012; Volume 14 ,937-954. · Zbl 1270.60080
[11] Altiok, T.; On the phase-type approximations of general distributions; IIE Trans.: 1985; Volume 17 ,110-116.
[12] Altiok, T.; Queueing modeling of a single processor with failures; Perform. Eval.: 1989; Volume 9 ,93-102. · Zbl 0667.68049
[13] Altiok, T.; ; Performance Analysis of Manufacturing Systems. Springer Series in Operations Research: New York, NY, USA 1997; . · Zbl 0942.90003
[14] Dallery, Y.; On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions; Queueing Syst.: 1994; Volume 15 ,199-209. · Zbl 0798.90077
[15] Economou, A.; Fakinos, D.; A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes; Eur. J. Oper. Res.: 2003; Volume 149 ,625-640. · Zbl 1030.60069
[16] Economou, A.; Fakinos, D.; Alternative approaches for the transient analysis of Markov chains with catastrophes; J. Stat. Theory Pract.: 2008; Volume 2 ,183-197. · Zbl 1420.60099
[17] Kyriakidis, E.; Dimitrakos, T.; Computation of the optimal policy for the control of a compound immigration process through total catastrophes; Methodol. Comput. Appl. Probab.: 2005; Volume 7 ,97-118. · Zbl 1107.90039
[18] Krishna Kumar, B.; Vijayakumar, A.; Sophia, S.; Transient analysis for state-dependent queues with catastrophes; Stoch. Anal. Appl.: 2008; Volume 26 ,1201-1217. · Zbl 1153.60394
[19] Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Ricciardi, L.M.; A note on birth-death processes with catastrophes; Stat. Probab. Lett.: 2008; Volume 78 ,2248-2257. · Zbl 1283.60110
[20] Zeifman, A.; Korotysheva, A.; Perturbation bounds for Mt/Mt/N queue with catastrophes; Stoch. Models: 2012; Volume 28 ,49-62. · Zbl 1243.60076
[21] Zeifman, A.; Satin, Y.; Panfilova, T.; Limiting characteristics for finite birth-death-catastrophe processes; Math. Biosci.: 2013; Volume 245 ,96-102. · Zbl 1308.92092
[22] Giorno, V.; Nobile, A.G.; Pirozzi, E.; A state-dependent queueing system with asymptotic logarithmic distribution; J. Math. Anal. Appl.: 2018; Volume 458 ,949-966. · Zbl 1388.60151
[23] Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Ricciardi, L.M.; On time non-homogeneous stochastic processes with catastrophes; Cybernetics and Systems 2010, Proceedings of the Austrian Society for Cybernetics Studies (EMCSR 2010), Vienna, Austria, 6-9 April 2010: Vienna, Austria 2010; ,169-174.
[24] Giorno, V.; Nobile, A.G.; Spina, S.; On some time non-homogeneous queueing systems with catastrophes; Appl. Math. Comput.: 2014; Volume 245 ,220-234. · Zbl 1335.90018
[25] Dimou, S.; Economou, A.; The single server queue with catastrophes and geometric reneging; Methodol. Comput. Appl. Probab.: 2013; Volume 15 ,595-621. · Zbl 1273.90053
[26] Giorno, V.; Nobile, A.G.; Ricciardi, L.M.; On some time-non-homogeneous diffusion approximations to queueing systems; Adv. Appl. Probab.: 1987; Volume 19 ,974-994. · Zbl 0655.60084
[27] Liu, X.; Gong, Q.; Kulkarni, V.G.; Diffusion models for double-ended queues with renewal arrival processes; Stoch. Syst.: 2015; Volume 5 ,1-61. · Zbl 1331.60177
[28] Büke, B.; Chen, H.; Fluid and diffusion approximations of probabilistic matching systems; Queueing Syst.: 2017; Volume 86 ,1-33. · Zbl 1373.60151
[29] Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Ricciardi, L.M.; On the M/M/1 queue with catastrophes and its continuous approximation; Queueing Syst.: 2003; Volume 43 ,329-347. · Zbl 1016.60080
[30] Dharmaraja, S.; Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; A continuous-time Ehrenfest model with catastrophes and its jump-diffusion approximation; J. Stat. Phys.: 2015; Volume 161 ,326-345. · Zbl 1329.60302
[31] Abramowitz, M.; Stegun, I.; ; Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables: New York, NY, USA 1972; . · Zbl 0543.33001
[32] Irwin, J.O.; The frequency-distribution of the difference between two independent variates following the same Poisson distribution; J. R. Stat. Soc.: 1937; Volume 100 ,415-416. · JFM 63.0512.03
[33] Skellam, J.G.; The frequency-distribution of the difference between two Poisson variates belonging to different populations distribution; J. R. Stat. Soc.: 1946; Volume 109 ,296. · Zbl 0063.07068
[34] Buonocore, A.; Di Crescenzo, A.; Giorno, V.; Nobile, A.G.; Ricciardi, L.M.; A Markov chain-based model for actomyosin dynamics; Sci. Math. Jpn.: 2009; Volume 70 ,159-174. · Zbl 1180.60075
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.