The intensity conservation law for queues with randomly changed service rate

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Abstract
König et al. (1978) have derived the so-called intensity conservation law in a stationary process connected with a marked point process (PMP). That law has been shown to be useful in obtaining invariance relations in queues (cf. Franken et al. (1981)). In this paper, somewhat different versions of the intensity conservation laws are derived for a stationary process with jump points. These laws are applied to queues with randomly changed service rate. As special cases, most of equations obtained by König et al.'s law can be derived from this law. Also, we derive some inequalities between characteristic quantities in a queue with a simple type of randomly changed service rate.