Non-ergodic Jackson Networks with Infinite Supply - Local Stabilization and Local Equilibrium Analysis

Classical Jackson networks are a well established tool for the analysis of complex systems. In this paper we analyze Jackson networks with the additional features that (i) nodes may have an in nite supply of low priority work and (ii) nodes may be unstable in the sense that the queue length at these nodes grows beyond any bound. We provide the limiting distribution of the queue length distribution at stable nodes, which turns out to be of product-form. A key step in establishing this result is the development of a new algorithm based on adjusted trac equations for detecting instable nodes. Our results complement the results known in the literature for the sub-cases of Jackson networks with either innite supply nodes or unstable nodes by providing an analysis of the signicantly more challenging case of networks with both types of nonstandard nodes present. Building on our product-form results, we provide closed-form solutions for common customer and system oriented performance measures

Unofficial trade when states are weak: the case of cross-border commerce in the Horn of Africa

This paper addresses informal cross-border trade in the Horn of Africa, with an emphasis on the Somalia borderlands. It will be shown that despite the collapse of a government in 1991, Somalia’s unofficial exports of cattle to Kenya have grown considerably during the past 13 years.Qoraalkani wuxuu ka hadlayaa ganacsiga ka gudbo xuduudaha Geeska Afrika. Gaar ahaan markii uu dhacay taliskii militeriga waxaa aad u sii kordhay xoolixii soomaaliyeed ee loo suuq geynaayay Kenya.Questo documento è dedicato al commercio transnazionale informale nel Corno D'Africa, con particolare attenzione ai confini della Somalia. Si dimostra che nonostante la caduta del governo nel 1991, le esportazioni di bestiame non ufficiali somale in Kenya sono aumentate considerevolmente durante gli ultimi 13 anni

Sojourn times in queueing networks

From a customer's point of view, the most important performance measure in a queueing network is his sojourn time. This paper presents a survey of sojourn time results in queueing networks. Particular attention is paid to product-form networks, for which exact expressions for the joint distribution of a customer's successive sojourn times along a quasi overtake-free path are discussed. When the non-overtaking condition is violated, or when no product form exists, few analytical results are known. The paper mentions some of these results, as weil as approximation techniques for product-form networks. For networks without product form, the emphasis is put on computational techniques and on some quite general approximation methods which have recently been adapted to the sojourn time problem

The cyclic queue and the tandem queue

We consider a closed queueing network, consisting of two FCFS single server queues in series: a queue with general service times and a queue with exponential service times. A fixed number N of customers cycle through this network. We determine the joint sojourn time distribution of a tagged customer in, first, the general queue and, then, the exponential queue. Subsequently, we indicate how the approach toward this closed system also allows us to study the joint sojourn time distribution of a tagged customer in the equivalent open two-queue system, consisting of FCFS single server queues with general and exponential service times, respectively, in the case that the input process to the first queue is a Poisson process