Performance analysis approximation in a queueing system of type M/G/1

Mathematical Methods of Operations Research

Volumn 63, Issue 2, 2006, Pages 341-356

  Bouallouche Medjkoune, Louiza ^a   Aissani, Djamil ^a  

^a UNIVERSITY OF BEJAIA   (Algeria)

Author keywords

Approximation; M G 1 queue; Perturbation; Size stationary distribution; Strong stability

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; ERROR ANALYSIS; PERTURBATION TECHNIQUES;

M/G/1 QUEUE; QUEUEING SYSTEM; SIZE STATIONARY DISTRIBUTION; STRONG STABILITY;

QUEUEING NETWORKS;

EID: 33646689608     PISSN: 14322994     EISSN: 14325217     Source Type: Journal    
DOI: 10.1007/s00186-005-0022-8     Document Type: Article

References (21)

1. Aïssani D, Kartashov NV (1983) Ergodicity and stability of Markov chains with respect to operator topologies in space of transition Kernels. Dokl Akad Nauk Ukr SSR Ser A, No 11:3-5 (Russian)
2. Aïssani D, Kartashov NV (1984) A strong stability of imbedded Markov chain in the M/G/1 queueing system. Teor. Veroyatnost. i Mat. Statist. 29,
3. English translation in Theory Probab Math Statist 29:3-7
4. Borovkov AA (Ed.) (1984) Asymptotic methods in queueing theory. Wiley, New York
5. Carson JS, Banks J, Nelson BL (1996) Discrete-event system simulation. 2nd edn. Prentice-Hall, New Jersey
6. Franken P (1970) Ein stetigkeitssatz für Verlustsusteme. Operations-forschung and Math Stat 11:1-23
7. Gelenbe E, Pujolle G (1998) Introduction to queueing networks. Wiley, New York
8. Gnedenko BV (1970) Sur certains problèmes non résolus de la théorie de files d'attente. Six International Telegraphic Congress, Munich
9. Hokstad P (1978) Approximation for the M/G/m queues. Opes Res 26:510-523
10. Ipsen CF, Meyer D (1994) Uniform stability of Markov chains. Siam J Matrix Ana Appl 15 No4:1061-1074
11. Kalashnikov VV, Tsitsiachvili GC (1972) Sur la stabilité des systèmes de files d'attente relativement à leurs fonctions de répartition perturbées. J Izv AN USSR Technique Cybernétique No2:41-49
12. Kartashov NV (1986) Strongly stable Markov chains. J Soviet Mat 34:1493-1498
13. Kartashov NV (1996) Strong stable Markov chains. VSP, Utrecht; TBiMC scientific, Kiev
14. Kennedy D (1972) The continuity of the single server queue. J Appl Prob 9, No3:370-381
15. Kovalenko IN, Kouznetsov NY, Shurenkov VM (1983) Stochastic processes. Naukovo Doumka Ed, Kiev
16. Rachev ST (1989) The problem of stability in Queueing theory. Queueing Syst 4:287-318
17. Rossberg HJ (1965) Über die Verteilung Von Wartereiten. Mathematische Nachrichten. 20, No 1/2:1-16
18. Stoyan D (1977) Ein Stetigkeitssatz für einlinige Wartemodelle der Bedienungstheorie. Math Operations Forsch u Statist No2:103-111
19. Stoyan D (1984) Comparison methods for queues and other stochastic models. English translation Daley DJ (ed) Wiley, New York
20. Wismer DA, Chattergy R (1978) Introduction to nonlinear optimization. Elsevier Ed., North Holland Inc., New York
21. Zolotariev VM (1975) On the continuity of stochastic sequences generated by recurrence procedures. J Theory Prob Appl T.20, No 4:834-847