Geodesic
Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty$ queue
Applications of Mathematics, Tome 33 (1988) no. 1, pp. 68-76
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For a discrete modified $GI/GI/c/\infty$ queue, $1\leq c \infty$, where the service times of all customers served during any busy period are independent random variables with not necessarily identical distribution functions, the joint distribution of the busy period, the subsequent idle period and the number of customers served during the busy period is derived. The formulae presented are in a convenient form for practical use. The paper is a continuation of [5], where the $M/GI/c/\infty$ discrete modified queue has been studied.
For a discrete modified $GI/GI/c/\infty$ queue, $1\leq c \infty$, where the service times of all customers served during any busy period are independent random variables with not necessarily identical distribution functions, the joint distribution of the busy period, the subsequent idle period and the number of customers served during the busy period is derived. The formulae presented are in a convenient form for practical use. The paper is a continuation of [5], where the $M/GI/c/\infty$ discrete modified queue has been studied.
DOI : 10.21136/AM.1988.104287
Classification : 60K25, 90B22
Keywords: distribution of the busy period; idle period; number of customers 
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Dvurečenskij, Anatolij. Joint distribution of the busy and idle periods of a discrete modified $GI/GI/c/\infty$ queue. Applications of Mathematics, Tome 33 (1988) no. 1, pp. 68-76. doi: 10.21136/AM.1988.104287

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