Name
Title | ||
|---|---|---|
On Multiserver retrial Queues: History, Okubo-Type hypergeometric Systems and Matrix Continued-fractions. |
Abstract | ||
|---|---|---|
In this paper, we study two families of QBD processes with linear rates: (a) the multiserver retrial queue and its easier relative; and (b) the multiserver M/M/infinity Markov modulated queue. The linear rates imply that the stationary probabilities satisfy a recurrence with linear coefficients; as known from previous work, they yield a "minimal/nondominant" solution of this recurrence, which may be computed numerically by matrix continued-fraction methods. Furthermore, the generating function of the stationary probabilities satisfies a linear differential system with polynomial coefficients, which calls for the venerable but still developing theory of holonomic (or D-finite) linear differential systems. We provide a differential system for our generating function that unifies problems (a) and (b), and we also include some additional features and observe that in at least one particular case we get a special "Okubo-type hypergeometric system", a family that recently spurred considerable interest. The differential system should allow further study of the Taylor coefficients of the expansion of the generating function at three points of interest: (i) the irregular singularity at 0; (ii) the dominant regular singularity, which yields asymptotic series via classic methods like the Frobenius vector expansion; and (iii) the point 1, whose Taylor series coefficients are the factorial moments. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1142/S0217595914400016 | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH |
Keywords | Field | DocType |
Retrial queue,stationary probabilities,Okubo hypergeometric system,minimal solution | Generating function,Mathematical optimization,Hypergeometric distribution,Matrix (mathematics),Markov chain,Singularity,Asymptotic expansion,Mathematics,Retrial queue,Taylor series | Journal |
Volume | Issue | ISSN |
31 | 2 | 0217-5959 |
Citations | PageRank | References |
3 | 0.47 | 12 |
Authors | ||
3 | ||