In this paper we consider the MMAP/PH/1 priority queue, both the case of preemptive resume and the case of non-preemptive service. The main idea of the presented analysis procedure is that the sojourn time of the low priority jobs in the preemptive case (and the waiting time distribution in the nonpreemptive case) can be represented by the duration of the busy period of a special Markovian flui...

With M(t) := sups∈[0,t] A(s)− s denoting the running maximum of a fractional Brownian motion A(·) with negative drift, this paper studies the rate of convergence of P(M(t)> x) to P(M > x). We define two metrics that measure the distance between the (complementary) distribution functions P(M(t) > ·) and P(M > ·). Our main result states that both metrics roughly decay as exp(−θt), where θ is the ...

BACKGROUND Spousal bereavement is documented as a highly stressful event. This article presents findings from research that explored bereavement survivors' perspectives on what support factors were most helpful to them. METHODS A qualitative telephone survey was conducted with caregiver spouses of Cittamani Hospice Service clients who died during 2005 and 2006. RESULTS Partner loss results ...

We provide a large deviation result for a random sum ∑Nx n=0Xn, 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 sq...

This paper deals with a discrete-time bulk-service Geo/Geo/1 queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time n. The service times both in a working vacation and in a busy period and the ...

In a financial market, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. For agents with long investment horizons, and under normal market conditions, trades may only occur infrequently, while for other agents, or at times of severe market stress, the timescales involved may be much shorter. We argue that in either case the use of ...

We consider a make-to-stock production-inventory model with one machine that produces stock in a buffer. The machine is subject to breakdowns. During up periods, the machine fills the buffer at a level-dependent rate α(x) > 0. During down periods, the production rate is zero, and the demand rate is either β(x) > 0 or γ(x) > 0 when the inventory level is x; which of the two demand rates applies ...

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We derive in this paper the transient queue length and the busy period distributions in the single server queue with phase-type (PH) services times and a batch Markovian arrival process (BMAP). These distributions are obtained by the uniformization technique which gives simple recurrence relations. The main advantage of this technique is that it leads to stable algorithms for which the precisio...

We propose a new Distributed Denial of Service (DDoS) defense mechanism that protects http web servers from application-level DDoS attacks based on the two methodologies: whitelist-based admission control and busy period-based attack flow detection. The attack flow detection mechanism detects attach flows based on the symptom or stress at the server, since it is getting more difficult to identi...