Skip to main content
Erschienen in: Queueing Systems 3-4/2020

10.07.2020

Matching queues with reneging: a product form solution

verfasst von: Francisco Castro, Hamid Nazerzadeh, Chiwei Yan

Erschienen in: Queueing Systems | Ausgabe 3-4/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Motivated by growing applications in two-sided markets, we study a parallel matching queue with reneging. Demand and supply units arrive to the system and are matched in an FCFS manner according to a compatibility graph specified by an N-system. If they cannot be matched upon arrival, they queue and may abandon the system as time goes by. We derive explicit product forms of the steady-state distributions of this system by identifying a partial balance condition.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Adan, I., Weiss, G.: Exact FCFS matching rates for two infinite multitype sequences. Operat. Res. 60(2), 475–489 (2012)CrossRef Adan, I., Weiss, G.: Exact FCFS matching rates for two infinite multitype sequences. Operat. Res. 60(2), 475–489 (2012)CrossRef
2.
Zurück zum Zitat Adan, I., Weiss, G.: A skill based parallel service system under FCFS–ALIS–steady state, overloads, and abandonments. Stoch. Syst. 4(1), 250–299 (2014)CrossRef Adan, I., Weiss, G.: A skill based parallel service system under FCFS–ALIS–steady state, overloads, and abandonments. Stoch. Syst. 4(1), 250–299 (2014)CrossRef
3.
Zurück zum Zitat Adan, I., Foley, R.D., McDonald, D.R.: Exact asymptotics for the stationary distribution of a Markov chain: a production model. Queueing Syst. 62(4), 311–344 (2009)CrossRef Adan, I., Foley, R.D., McDonald, D.R.: Exact asymptotics for the stationary distribution of a Markov chain: a production model. Queueing Syst. 62(4), 311–344 (2009)CrossRef
4.
Zurück zum Zitat Adan, I., Bušić, A., Mairesse, J., Weiss, G.: Reversibility and further properties of FCFS infinite bipartite matching. Math. Operat. Res. 43(2), 598–621 (2017)CrossRef Adan, I., Bušić, A., Mairesse, J., Weiss, G.: Reversibility and further properties of FCFS infinite bipartite matching. Math. Operat. Res. 43(2), 598–621 (2017)CrossRef
5.
Zurück zum Zitat Adan, I., Kleiner, I., Righter, R., Weiss, G.: FCFS parallel service systems and matching models. Perform. Eval. 127, 253–272 (2018)CrossRef Adan, I., Kleiner, I., Righter, R., Weiss, G.: FCFS parallel service systems and matching models. Perform. Eval. 127, 253–272 (2018)CrossRef
6.
Zurück zum Zitat Adan, I., Boon, M.A.A., Weiss, G.: Design heuristic for parallel many server systems. Euro. J. Operat. Res. 273(1), 259–277 (2019)CrossRef Adan, I., Boon, M.A.A., Weiss, G.: Design heuristic for parallel many server systems. Euro. J. Operat. Res. 273(1), 259–277 (2019)CrossRef
7.
Zurück zum Zitat Afèche, P., Diamant, A., Milner, J.: Double-sided batch queues with abandonment: modeling crossing networks. Operat. Res. 62(5), 1179–1201 (2014)CrossRef Afèche, P., Diamant, A., Milner, J.: Double-sided batch queues with abandonment: modeling crossing networks. Operat. Res. 62(5), 1179–1201 (2014)CrossRef
8.
Zurück zum Zitat Afèche, P., Caldentey, R., Gupta, V.: On the optimal design of a bipartite matching queueing system. Available at SSRN 3345302, (2019) Afèche, P., Caldentey, R., Gupta, V.: On the optimal design of a bipartite matching queueing system. Available at SSRN 3345302, (2019)
9.
Zurück zum Zitat Boxma, O.J., David, I., Perry, D., Stadje, W.: A new look at organ transplantation models and double matching queues. Probab. Eng. Inform. Sci. 25(2), 135–155 (2011)CrossRef Boxma, O.J., David, I., Perry, D., Stadje, W.: A new look at organ transplantation models and double matching queues. Probab. Eng. Inform. Sci. 25(2), 135–155 (2011)CrossRef
10.
Zurück zum Zitat Caldentey, R.A., Kaplan, E.H.: A heavy traffic approximation for queues with restricted customer-server matchings. Working paper, (2007) Caldentey, R.A., Kaplan, E.H.: A heavy traffic approximation for queues with restricted customer-server matchings. Working paper, (2007)
11.
Zurück zum Zitat Fazel-Zarandi, M.M., Kaplan, E.H.: Approximating the first-come, first-served stochastic matching model with Ohm’s law. Operat. Res. 66(5), 1423–1432 (2018)CrossRef Fazel-Zarandi, M.M., Kaplan, E.H.: Approximating the first-come, first-served stochastic matching model with Ohm’s law. Operat. Res. 66(5), 1423–1432 (2018)CrossRef
12.
Zurück zum Zitat Gardner, K., Righter, R.: Product forms for FCFS queueing models with arbitrary server-job compatibilities: An overview. arXiv preprint arXiv:2006.05979 (2020) Gardner, K., Righter, R.: Product forms for FCFS queueing models with arbitrary server-job compatibilities: An overview. arXiv preprint arXiv:​2006.​05979 (2020)
13.
Zurück zum Zitat Gardner, K., Zbarsky, S., Doroudi, S., Harchol-Balter, M., Hyytiä, E., Scheller-Wolf, A.: Queueing with redundant requests: exact analysis. Queueing Syst. 83(3–4), 227–259 (2016)CrossRef Gardner, K., Zbarsky, S., Doroudi, S., Harchol-Balter, M., Hyytiä, E., Scheller-Wolf, A.: Queueing with redundant requests: exact analysis. Queueing Syst. 83(3–4), 227–259 (2016)CrossRef
14.
Zurück zum Zitat Green, L.: A queueing system with general-use and limited-use servers. Operat. Res. 33(1), 168–182 (1985)CrossRef Green, L.: A queueing system with general-use and limited-use servers. Operat. Res. 33(1), 168–182 (1985)CrossRef
15.
Zurück zum Zitat Jackson, J.R.: Networks of waiting lines. Operat. Res. 5(4), 518–521 (1957) Jackson, J.R.: Networks of waiting lines. Operat. Res. 5(4), 518–521 (1957)
16.
Zurück zum Zitat Jackson, J.R.: Jobshop-like queueing systems. Manag. Sci. 10(1), 131–142 (1963)CrossRef Jackson, J.R.: Jobshop-like queueing systems. Manag. Sci. 10(1), 131–142 (1963)CrossRef
17.
Zurück zum Zitat Kaplan, E.H.: A public housing queue with reneging. Decis. Sci. 19(2), 383–391 (1988)CrossRef Kaplan, E.H.: A public housing queue with reneging. Decis. Sci. 19(2), 383–391 (1988)CrossRef
18.
Zurück zum Zitat Mairesse, J., Moyal, P.: Stability of the stochastic matching model. J. Appl. Probab. 53(4), 1064–1077 (2016)CrossRef Mairesse, J., Moyal, P.: Stability of the stochastic matching model. J. Appl. Probab. 53(4), 1064–1077 (2016)CrossRef
19.
Zurück zum Zitat Moyal, P., Busic, A., Mairesse, J.: A product form and a sub-additive theorem for the general stochastic matching model. arXiv preprint arXiv:1711.02620 (2017) Moyal, P., Busic, A., Mairesse, J.: A product form and a sub-additive theorem for the general stochastic matching model. arXiv preprint arXiv:​1711.​02620 (2017)
20.
Zurück zum Zitat Talreja, R., Whitt, W.: Fluid models for overloaded multiclass many-server queueing systems with first-come, first-served routing. Manag. Sci. 54(8), 1513–1527 (2008)CrossRef Talreja, R., Whitt, W.: Fluid models for overloaded multiclass many-server queueing systems with first-come, first-served routing. Manag. Sci. 54(8), 1513–1527 (2008)CrossRef
21.
Zurück zum Zitat Visschers, J., Adan, I., Weiss, G.: A product form solution to a system with multi-type jobs and multi-type servers. Queueing Syst. 70(3), 269–298 (2012)CrossRef Visschers, J., Adan, I., Weiss, G.: A product form solution to a system with multi-type jobs and multi-type servers. Queueing Syst. 70(3), 269–298 (2012)CrossRef
22.
Zurück zum Zitat Zenios, S.A.: Modeling the transplant waiting list: a queueing model with reneging. Queueing Syst. 31(3–4), 239–251 (1999)CrossRef Zenios, S.A.: Modeling the transplant waiting list: a queueing model with reneging. Queueing Syst. 31(3–4), 239–251 (1999)CrossRef
23.
Zurück zum Zitat Zhan, D., Weiss, G.: Many-server scaling of the N-system under FCFS-ALIS. Queueing Syst. 88(1–2), 27–71 (2018)CrossRef Zhan, D., Weiss, G.: Many-server scaling of the N-system under FCFS-ALIS. Queueing Syst. 88(1–2), 27–71 (2018)CrossRef
Metadaten
Titel
Matching queues with reneging: a product form solution
verfasst von
Francisco Castro
Hamid Nazerzadeh
Chiwei Yan
Publikationsdatum
10.07.2020
Verlag
Springer US
Erschienen in
Queueing Systems / Ausgabe 3-4/2020
Print ISSN: 0257-0130
Elektronische ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-020-09662-y

Weitere Artikel der Ausgabe 3-4/2020

Queueing Systems 3-4/2020 Zur Ausgabe

Premium Partner