2005/06/02 by Vyacheslav M. Abramov, Abramov, Vyacheslav M.
Business, Management and Accounting · Computer Science · Mathematics · #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Network Traffic and Congestion Control #Probability (math.PR) #Wireless Communication Networks Research #math.PR #msc:60K25
paper · pdf · doi:10.48550/arxiv.math/0506033
29 pages, 6 pictures. The paper is substantially revised according to a large number of comments of referees
openalex publication_date 2005/06/02 · arxiv created 2010/03/24 · arxiv updated 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The M/GI/m/n queueing system with m homogeneous servers and the finite number n of waiting spaces is studied. Let λ be the customers arrival rate, and let μ be the reciprocal of the expected service time of a customer. Under the assumption λ=mμ it is proved that the expected number of losses during a busy period is the same value for all n≥1, while in the particular case of the Markovian system M/M/m/n the expected number of losses during a busy period is (mm)/(m!) for all n≥0. Under the additional assumption that the probability distribution function of a service time belongs to the class NBU or NWU, the paper establishes simple inequalities for those expected numbers of losses in M/GI/m/n queueing systems.