Complutense University Library

Performance of two-stage tandem queues with blocking: The impact of several flows of signals


Gómez-Corral, Antonio and Escribano Martos, Manuel David (2006) Performance of two-stage tandem queues with blocking: The impact of several flows of signals. Performance Evaluation, 63 . pp. 910-938. ISSN 0166-5316

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


This paper considers a two-stage tandem G-queue with blocking, service requirements of phase type and arrivals of units and of signals - which cancel one unit waiting in line or in service - both assumed to be Markovian arrival processes. The main characteristic of the service process in this tandem queue is blocking, which occurs according to a BAS (blocking after service) mechanism. A finite queue of capacity K >= 0 is allowed between servers, so that a unit having completed processing on Station I attempts to join Station 2. If K + 1 units are accommodated into Station 2, then the completed unit is forced to wait at Station I occupying the server space until a space becomes available at Station 2. Thus the first server becomes blocked or not available for service on incoming units. Our purpose is to study the influence of several flows of signals on the performance evaluation of the queueing model through various probabilistic descriptors. By means of a numerical investigation, we study four two-stage tandem G-queues with blocking depending on the existence of flows of signals affecting Station 1 and/or Station 2. The essential tool in our analysis is the general theory of quasi-birth-and-death processes.

Item Type:Article
Uncontrolled Keywords:Blocking; Markovian arrival process; Phase type distribution; Quasi-birth-and-death process; Signals; Tandem queue
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15600

Queueing Networks with Finite Capacity Queues, I.F. Akyildiz, H.G. Perros (Eds.), Performance Evaluation 10 (3) (1989) 149–262 (special issue).

F. Albores, P. Bocharov, R. Ilhuicatzi, D. Lyubin, Analysis of a two-node exponential queueing network with blocking, in: Queues, Flows, Systems, Networks. Proceedings of the International Conference “Modern Mathematical Methods of Analysis and Optimization of Telecommunication Networks”, Gomel, 2003, pp. 11–17.

J.R. Artalejo, G-networks: A versatile approach for work removal in queueing networks, European Journal of Operational Research 126 (2000) 233–249.

B. Avi-Itzhak, M. Yadin, A sequence of two servers with no intermediate queue, Management Science 11 (1965) 553–564.

B. Avi-Itzhak, A sequence of service stations with arbitrary input and regular service times, Management Science 11 (1965) 565–571.

B. Avi-Itzhak, S. Halfin, Servers in tandem with communication and manufacturing blocking, Journal of Applied Probability 30 (1993)429–437.

B. Avi-Itzhak, H. Levy, A sequence of servers with arbitrary input and regular service times revisited, Management Science 41 (1995)1039–1047.

F. Avram, A. G´omez-Corral, On bulk-service MAP/PHL,N /1/N G-queues with repeated attempts, Annals of Operations Research 141 (2006) 117–149.

S. Balsamo, Properties and analysis of queueing network models with finite capacities, in: L. Donatiello, R. Nelson (Eds.), Performance Evaluation of Computer and Communication Systems, in: Lecture Notes in Computer Science, vol. 729, Springer-Verlag, 1994.

S. Balsamo, V. de Nitto Person´e, R. Onvural, Analysis of Queueing Networks with Blocking, Kluwer Academic Publishers, Boston, 2001.

S. Balsamo, V. de Nitto Person´e, P. Inverardi, A review on queueing network models with finite capacity queues for software architectures performance prediction, Performance Evaluation 51 (2003) 269–288.

Deposited On:13 Jun 2012 08:01
Last Modified:08 Mar 2016 15:52

Repository Staff Only: item control page