Diffusion approximation for a processor sharing queue in heavy traffic

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We show that under mild assumptions, including standard heavy traffic assumptions, the (suitably rescaled) measure valued processes corresponding to a sequence of processor sharing queues converge in distribution to a measure valued diffusion process. The limiting process is characterized as the image under an appropriate lifting map, of a one-dimensional reflected Brownian motion. As an immediate consequence, one obtains a diffusion approximation for the queue length process of a processor sharing queue

Monetary Policy and Public Finances: Inflation Targets in a New Perspective

This paper examines how the private sector, the monetary authority, and the fiscal authority interact and concludes that unrestricted central bank independence may not be an optimal way to collect seigniorage revenues or stabilize supply shocks. Moreover, the paper shows that the implementation of an optimal inflation target results in optimal shares of government finances--seigniorage, taxes, and the spending shortfall--from society's point of view but still involves suboptimal stabilization. Even if price stability is the sole central bank objective, a positive inflation target has important implications for the government's finances, as well as for stabilization. Copyright 1999, International Monetary Fund

Invariance of fluid limits for the Shortest Remaining Processing Time and Shortest Job First policies

We consider a single-server queue with renewal arrivals and i.i.d. service times, in which the server employs either the preemptive Shortest Remaining Processing Time (SRPT) policy, or its non-preemptive variant, Shortest Job First (SJF). We show that for given stochastic primitives (initial condition, arrival and service processes), the model has the same fluid limit under either policy. In particular, we conclude that the well-known queue length optimality of preemptive SRPT is also achieved, asymptotically on fluid scale, by the simpler-to-implement SJF policy. We also conclude that on fluid scale, SJF and SRPT achieve the same performance with respect to response times of the longest-waiting jobs in the system.Comment: 24 page

Heavy traffic limit for a processor sharing queue with soft deadlines

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.Comment: Published at http://dx.doi.org/10.1214/105051607000000014 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Natural disasters and growth: evidence using a wide panel of countries

Large natural disasters (LNDs) are ubiquitous phenomena with potentially large impacts on the infrastructure and population of countries, and on their economic activity in general. I examine the occurrence pattern of several types of disasters on a panel of 113 countries and its relationship with economic growth using data ranging from 1960 to 1996. The disasters are earthquakes, floods, slides, volcano eruptions, tsunamis, wind storms, wild fires and extreme temperatures. The country sample is partitioned in two ways: small, medium and large population; and low, medium and high income. The results suggest a heterogeneous pattern of short and long-term impact of LNDs, depending on the per capita GDP, the size of the countries studied and the type of LND. Overall, and contrary to previous research, LNDs appear to have persistent effects on the rate of GDP growth in the period between 1960 and 1996. These effects range from a decrease of 0.9% to an increase of 0.6%, depending on the type of disaster.Natural disasters, catastrophes, growth, foreign aid, panel data