A 32-year-old woman with severe foot pain came to our emergency department after a busy night duty in hospital followed by an extended sleep period. Physical examination revealed a discrete swelling of the medial aspect of the right foot and a painful plantar arch during digital examination. Magnetic resonance imaging (MRI) with intravenous gadolinium showed filling defects in the lateral plant...

We provide a large deviation result for a random sum ∑ Nx n=0 Xn, where Nx is a renewal counting process and {Xn}n≥0 are i.i.d. random variables, independent of Nx, with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than e− √ x and have zero relative decrease in intervals of length √ x, hence ...

This paper is devoted to a study of the integral of the workload process of the single server queue, in particular during one busy period. Firstly, we find asymptotics of the area A swept under the workload processW (t) during the busy period when the service time distribution has a regularly varying tail. We also investigate the case of a light-tailed service time distribution. Secondly, we co...

The M/GI/m/n queueing system with m homogeneous servers and the finite number n of waiting spaces is studied. Let λ be the customers arrival rate, and let μ be the reciprocal of the expected service time of a customer, where λ = mμ. The paper proves that under this assumption the expected number of losses during a busy period remains the same for all n ≥ 1, while in the particular case of the M...

Bernoulli feedback Queue and system lengths Busy periods Optimal control Tabu search a b s t r a c t This paper studies a Geo/G/1/∞ queueing system under an (m, N)-policy, i.e., the service station operates under an N-policy with an early setup where the startup period begins when m(≤ N) customers accumulate in the system. Moreover, it is assumed that the i-th service of each customer is either...