Processor sharing: A survey of the mathematical theory
Automation and Remote Control
The M/G/1 processor-sharing queue with disasters
Computers & Mathematics with Applications
On busy period and sojourn time distributions in the M/G/1-EPS queue with catastrophes
Automation and Remote Control
| Hi-index | 0.00 |
We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author's monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author's work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.