Comparison of two randomized policy \(M/G/1\) queues with second optional service, server breakdown and startup
The aim of this paper is to compare two optimal policies: \((T,p)\)-policy and \((p,N)\)-policy for \(M/G/1\) queues with an unreliable server, a second optional service, and general startup times. All customers that arrive in the system demand a first (required) service, and only some of customers require a second (optional) service. The server needs a startup time before providing the first required service. As soon as the system becomes empty after servicing all customers, the server takes a vacation, and the system operates according to one of the policies \((T,p)\) or \((p,N)\). The \((T,p)\)-policy is an extension of \(T\)-policy (the case \(p=1\)), which has been introduced by \textit{D. P. Heyman} [Manag. Sci. 23, 775--778 (1977; Zbl 0357.60022)]. The \((T,p)\)-policy is characterized as follows. If the server is empty, then the server is switched off and the vacation time \(T\) is required, which is repeated if there is no arrival during this time \(T\). If there is at least one arrival, then the server is switched on with probability \(p\), or with complementary probability \(1-p\) remains to be switched off. The \((p,N)\)-policy is defined as follows. As the system becomes empty, the server is turned off. If upon arrival of a customer in the system, the total number of customers reaches \(N\), then the server is turned on with probability \(p\), and with the complementary probability \(1-p\) remains to be switched off. The papers finds closed form for joint optimal solutions (defined explicitly in the paper) for these two policies. It is shown that under optimal operating conditions, the \((p,N)\)-policy has a lower cost than that of the \((T,p)\)-policy.
scientific article; zbMATH DE number 5702042
scientific article