The erlangization method for Markovian fluid flows

Ramaswami, V.; Woolford, Douglas G.; Stanford, David A.

doi:10.1007/s10479-008-0309-2

Cited by 43 publications

(38 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show that the specification of this implementation delay to be of mixed Erlang nature improves the tractability of the resulting expression for the Laplace transform of the Parisian ruin time. In nature, this is similar to the use of Erlangian horizons (rather than a deterministic horizon) for the calculation of finite-time ruin probabilities in various risk models (see Asmussen et al (2002) and Ramaswami et al (2008)). As will be shown, all our results are expressed in terms of scale functions for which many explicit examples are known; see, e.g., Hubalek and Kyprianou (2010), Kyprianou and Rivero (2008), as well as the numerical algorithm developed by Surya (2008).…”

Section: Introductionmentioning

confidence: 99%

An Insurance Risk Model with Parisian Implementation Delays

Landriault

Renaud

Zhou

2013

Methodol Comput Appl Probab

View full text Add to dashboard Cite

Abstract. Inspired by Parisian barrier options in finance (see e.g. Chesney et al. (1997)), a new definition of the event ruin for an insurance risk model is considered. As in Dassios and Wu (2009), the surplus process is allowed to spend time under a pre-specified default level before ruin is recognized. In this paper, we capitalize on the idea of Erlangian horizons (see Asmussen et al. (2002) and Kyprianou and Pistorius (2003)) and, thus assume an implementation delay of a mixed Erlang nature. Using the modern language of scale functions, we study the Laplace transform of this Parisian time to default in an insurance risk model driven by a spectrally negative Lévy process of bounded variation. In the process, a generalization of the two-sided exit problem for this class of processes is further obtained.

show abstract

Section: Introductionmentioning

confidence: 99%

An Insurance Risk Model with Parisian Implementation Delays

Landriault

Renaud

Zhou

2013

Methodol Comput Appl Probab

View full text Add to dashboard Cite

show abstract

“…In this section we briefly summarize the most essential results of [17] and [18] on the busy period analysis of fluid models.…”

Section: Busy Period Analysismentioning

confidence: 99%

“…According to Theorem 1 of [18], the LST of Ψ(t), denoted by Ψ * (s) satisfies the nonsymmetric algebraic Riccati equation…”

Section: Busy Period Analysismentioning

confidence: 99%

“…One can rely on a generic numerical Laplace transform inversion procedure, but according to our experience they are not always reliable up to the machine precision, and need complex arithmetic. Instead, a simple and elegant procedure called Erlangization is available [18], according to which the order-n approximation F (n)…”

Section: Busy Period Analysismentioning

confidence: 99%

“…For the detailed proof of the theorem, see [18]. The idea is to construct a special fluid model which counts the number of Exp(ν) events during the busy period.…”

Section: Busy Period Analysismentioning

confidence: 99%

See 2 more Smart Citations

Efficient analysis of the MMAP[K]/PH[K]/1 priority queue

Horváth

2015

European Journal of Operational Research

View full text Add to dashboard Cite

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 fluid model. By making use of the recent results on the busy period analysis of Markovian fluid models it is possible to calculate several queueing performance measures in an efficient way including the sojourn time distribution (both in the time domain and in the Laplace transform domain), the moments of the sojourn time, the generating function of the queue length, the queue length moments and the queue length probabilities.

show abstract

Double‐sided queues and their applications to vaccine inventory management

Wu,

He,

Erenay

2024

Naval Research Logistics

View full text Add to dashboard Cite

We consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.

show abstract

The erlangization method for Markovian fluid flows

Cited by 43 publications

References 20 publications

An Insurance Risk Model with Parisian Implementation Delays

An Insurance Risk Model with Parisian Implementation Delays

Efficient analysis of the MMAP[K]/PH[K]/1 priority queue

Double‐sided queues and their applications to vaccine inventory management

Contact Info

Product

Resources

About