The discrete busy period distribution for various single server queues
نویسندگان
چکیده
منابع مشابه
Limits and Approximations for the Busy-period Distribution in Single-server Queues
Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/1 queue, the complementary busy-period cdf is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as ρ → 1), where the scaling parameters are based on the asymptotics as t → ∞. We c...
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We obtain sufficient conditions for the finiteness of the moments of the single-server queue busy period in discrete and continuous time. In the cases of power and exponential moments, the conditions found coincide with the known necessary ones. 1. Introduction and notation. Consider a sequence t n n of random vectors with nonnegative coordinates which are i.i.d. in n, but any dependence betwee...
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This paper complements two previous studies (Daley and Rolski, 1984, 199 1) by indicating the extent to which characteristics of a general stationary point process taken as the arrival process of a single-server queue influence light traffic limit theorems for the two essentially distinct schemes of dilation and thinning as routes to the limit. Properties of both the work-load and the waiting-t...
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The expected wait in the Gi/G/1 queue is related to the mean and variance of the idle time. For arrival distributions which are 1FR or have mean residual life bounded by r-, simple bounds are obtained which A. give, for example, the expected number in queue to within at most one customer. By equating input with output, relations between random variables are used to obtain expressions foi the mo...
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In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biase...
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ژورنال
عنوان ژورنال: Applicationes Mathematicae
سال: 1965
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am-8-1-37-46