On the law of the iterated logarithm in multiphase queueing systems. II

Article type: Research Article

Authors: Minkevičius, Saulius

Affiliations: Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. E-mail: [email protected]

Abstract: Queueing systems with a single device are well developed (see, for example, Borovkov, 1972; 1980). But there are only several works in the theory of multiphase queueing systems in heavy traffic (see Iglehart, Whitt, 1970b) and no proof of laws of the iterated logarithm for the probabilistic characteristics of multiphase queuing systems in heavy traffic. The law of the iterated logarithm for the waiting time of a customer is proved in the first part of the paper (see Minkevičius, 1995). In this work, theorems on laws of the iterated logarithm for the other main characteristics of multiphase queuing systems in heavy traffic (a summary queue length of customers, a queue length of customers, a waiting time of a customer) are proved.

Keywords: multiphase queuing system, the law of the iterated logarithm, a summary queue length of customers, a queue length of customers, a waiting time of a customer

DOI: 10.3233/INF-1997-8304

Journal: Informatica, vol. 8, no. 3, pp. 367-376, 1997