Quasireversibility

In queueing theory, a discipline within the mathematical theory of probability, quasireversibility (sometimes QR) is a property of some queues. The concept was first identified by Richard R. Muntz[1] and further developed by Frank Kelly.[2][3] Quasireversibility differs from reversibility in that a stronger condition is imposed on arrival rates and a weaker condition is applied on probability fluxes. For example, an M/M/1 queue with state-dependent arrival rates and state-dependent service times is reversible, but not quasireversible.[4]

A network of queues, such that each individual queue when considered in isolation is quasireversible, always has a product form stationary distribution.[5] Quasireversibility had been conjectured to be a necessary condition for a product form solution in a queueing network, but this was shown not to be the case. Chao et al. exhibited a product form network where quasireversibility was not satisfied.[6]

  1. ^ Muntz, R.R. (1972). Poisson departure process and queueing networks (IBM Research Report RC 4145) (Technical report). Yorktown Heights, N.Y.: IBM Thomas J. Watson Research Center.
  2. ^ Kelly, F. P. (1975). "Networks of Queues with Customers of Different Types". Journal of Applied Probability. 12 (3): 542–554. doi:10.2307/3212869. JSTOR 3212869. S2CID 51917794.
  3. ^ Kelly, F. P. (1976). "Networks of Queues". Advances in Applied Probability. 8 (2): 416–432. doi:10.2307/1425912. JSTOR 1425912. S2CID 204177645.
  4. ^ Harrison, Peter G.; Patel, Naresh M. (1992). Performance Modelling of Communication Networks and Computer Architectures. Addison-Wesley. p. 288. ISBN 0-201-54419-9.
  5. ^ Kelly, F.P. (1982). Networks of quasireversible nodes Archived 2007-02-21 at the Wayback Machine. In Applied Probability and Computer Science: The Interface (Ralph L. Disney and Teunis J. Ott, editors.) 1 3-29. Birkhäuser, Boston
  6. ^ Chao, X.; Miyazawa, M.; Serfozo, R. F.; Takada, H. (1998). "Markov network processes with product form stationary distributions". Queueing Systems. 28 (4): 377. doi:10.1023/A:1019115626557. S2CID 14471818.