We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent r...

We consider a Jackson-type network, each of whose nodes contains N identical channels with a single server. Upon arriving at a node, a task selects m of the channels at random, and enters the one with the shortest queue. We provide stochastic bounds for the distribution of the state of the network in terms of the behaviour of independent nodes of the same type. The bounds are asymptotically tig...

Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for server j. We propose to extend Jackson networks by “branching” and by “control” features. Both extensions are new and substantially expand the modelling powe...

We examine the fundamental tension between efficiency and stability in social network formation. Jackson and Wolinsky (JET, 1996) showed that the component-wise egalitarian payoff rule supports an efficient network as being pairwise stable if and only if the network benefit function is critical link monotone. We extend this insight to strong pairwise stability and derive that the critical link ...

1.1. Rationale The Jackson network [1] is a basic model favored as a useful beginning approach to many queueing network problems. Its appeal stems from not only its product-form solution for the joint distribution of the number of customers in each queue but also from the simplicity of the structures of the model. Markovian routing is one such structure. The purpose of this paper is to study so...

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion ...

We introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, rules of network formation, and a dominance relation on feasible networks. Rules may range from noncooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates pla...

We study the stopping times of gossip algorithms fornetwork coding. We analyze algebraic gossip (i.e., random linearcoding) and consider three gossip algorithms for informationspreading: Pull, Push, and Exchange. The stopping time ofalgebraic gossip is known to be linear for the complete graph, butthe question of determining a tight upper bound or lower boundsfor general...

Homophily is the tendency of people to associate relatively more with those who are similar to them than with those who are not. In Golub and Jackson (2011), we introduced degree-weighted homophily (DWH), a new measure of this phenomenon, and showed that it gives a lower bound on the time it takes for a certain natural best-reply or learning process operating in a social network to converge. He...