2016/07/29 by Jori Selen, Selen, Jori, Brian Fralix +1
Business, Management and Accounting · Computer Science · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Wireless Communication Networks Research
paper · pdf · doi:10.48550/arxiv.1607.08722
openalex publication_date 2016/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the time-dependent behavior of an M/M/c priority queue having\ntwo customer classes, class-dependent service rates, and preemptive priority\nbetween classes. More particularly, we develop a method that determines the\nLaplace transforms of the transition functions when the system is initially\nempty. The Laplace transforms corresponding to states with at least c\nhigh-priority customers are expressed explicitly in terms of the Laplace\ntransforms corresponding to states with at most c - 1 high-priority\ncustomers. We then show how to compute the remaining Laplace transforms\nrecursively, by making use of a variant of Ramaswami's formula from the theory\nof M/G/1-type Markov processes. While the primary focus of our work is on\nderiving Laplace transforms of transition functions, analogous results can be\nderived for the stationary distribution: these results seem to yield the most\nexplicit expressions known to date.\n