The M/G/∞ Queue in Random Environment

• Published in: Information Technologies and Mathematical Modelling Vol. 487; pp. 312 - 324
• Main Authors: Nazarov, Anatoly, Baymeeva, Galina
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2014; Springer International Publishing
• Series: Communications in Computer and Information Science
• Subjects: general service-time; infinite-server queue; Maths for computer scientists; method of asymptotic analysis; method of screened flow; Probability & statistics; queueing theory; random environment; Systems analysis & design
• ISBN: 9783319136707; 3319136704
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-319-13671-4_36

Infinite-server queues are often used to approximate the behavior of systems with sufficiently large number of servers such as banks, call-centers, supermarkets or digital distribution platforms. Such systems often become subjects to external influences which affect their performance, particularly their arrival rate and service-time distribution. In this article we consider a mathematical model of such a situation as an M/G/ ∞ queue operating in a “random environment”, for which the underlying process is a continuous-time Markov chain with finite number of states. The arrival rate and service-time distribution change randomly according to the environment state. Note that distribution of service-time of customers, which are currently being served, does not change until the service-time is finished. The approximate probability distribution of the number of customers under certain conditions is obtained.