2016/10/04 by Reza Aghajani, Aghajani, Reza, Kavita Ramanan +1
Business, Management and Accounting · Decision Sciences · #60J70 #68M20 #90B15 #Advanced Queuing Theory Analysis #FOS: Mathematics #Primary 60K25 #Probability (math.PR) #Probability and Risk Models #secondary 90B22
paper · pdf · doi:10.48550/arxiv.1610.01118
openalex publication_date 2016/10/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We consider the so-called GI/GI/N queue, in which a stream of jobs with\nindependent and identically distributed service times arrive as a renewal\nprocess to a common queue that is served by N identical parallel servers in a\nfirst-come-first-serve manner. We introduce a new representation for the state\nof the system and, under suitable conditions on the service and interarrival\ndistributions, establish convergence of the corresponding sequence of centered\nand scaled stationary distributions in the so-called Halfin-Whitt asymptotic\nregime. In particular, this resolves an open question posed by Halfin and Whitt\nin 1981. We also characterize the limit as the stationary distribution of an\ninfinite-dimensional two-component Markov process that is the unique solution\nto a certain stochastic partial differential equation. Previous results were\nessentially restricted to exponential service distributions or service\ndistributions with finite support, for which the corresponding limit process\nadmits a reduced finite-dimensional Markovian representation. We develop a\ndifferent approach to deal with the general case when the Markovian\nrepresentation of the limit is truly infinite-dimensional. This approach is\nmore broadly applicable to a larger class of networks.\n