We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays . We describe the model as a bivariate Markov chain, prove its ergodicity and study the joint equilibrium distribution. We write a functional equation for the bivariate generating function, finding the solution on a subset of its domain. This solution allows us to prove that the equilibrium distribution of the chain decays super-exponentially fast in the quarter plane. We exploit the latter result and discuss the numerical computation of the solution through a simple yet effective approximation scheme in a wide region of the parameters. Finally, we compare the features of this queueing model with the standard M/D/1 system, showing that the congestion turns out to be very different when the traffic intensity is close to 1.

Lancia, C., Guadagni, G., Ndreca, S., Scoppola, B. (2018). Asymptotics for the late arrivals problem. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 88(3), 475-493 [10.1007/s00186-018-0643-3].

Asymptotics for the late arrivals problem

Lancia C.;Ndreca S.;Scoppola B.
2018-01-01

Abstract

We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays . We describe the model as a bivariate Markov chain, prove its ergodicity and study the joint equilibrium distribution. We write a functional equation for the bivariate generating function, finding the solution on a subset of its domain. This solution allows us to prove that the equilibrium distribution of the chain decays super-exponentially fast in the quarter plane. We exploit the latter result and discuss the numerical computation of the solution through a simple yet effective approximation scheme in a wide region of the parameters. Finally, we compare the features of this queueing model with the standard M/D/1 system, showing that the congestion turns out to be very different when the traffic intensity is close to 1.
2018
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
English
late arrivals; exponentially delayed arrivals; pre-scheduled random arrivals; Queues with correlated arrivals; bivariate generating function
Lancia, C., Guadagni, G., Ndreca, S., Scoppola, B. (2018). Asymptotics for the late arrivals problem. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 88(3), 475-493 [10.1007/s00186-018-0643-3].
Lancia, C; Guadagni, G; Ndreca, S; Scoppola, B
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
glns.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 1.43 MB
Formato Adobe PDF
1.43 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/246297
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact