An M/G/1 queue has arrivals at rate and a service time distribution given by FY(y). Assume that λ Z(z) be the distribution of the inter-renewal intervals and let E [Z] be the mean inter-renewal interval.
An M/G/1 queue has arrivals at rate and a service time distribution given by F Y (y). Assume that…
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a) Find the fraction of time that the system is empty as a function of and E [Z]. State carefully what you mean by such a fraction.
b) Apply Little’s theorem, not to the system as a whole, but to the number of customers in the server (i.e., 0 or 1). Use this to find the fraction of time that the server is busy.
c) Combine your results in a) and b) to find E [Z] in terms of and E [Y]; give the fraction of time that the system is idle in terms of and E [Y].
d) Find the expected duration of a busy period.
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