Braess's paradox in a queueing network with state-dependent routing

Abstract

We consider initially two parallel routes, each of two queues in tandem, with arriving customers choosing the route giving them the shortest expected time in the system, given the queue lengths at the customer's time of arrival. All interarrival and service times are exponential.We then augment this network to obtain a Wheatstone bridge, in which customers may cross from one route to the other between queues, again choosing the route giving the shortest expected time in the system, given the queue lengths ahead of them.We find that Braess's paradox can occur: namely in equilibrium the expected transit time in the augmented network, for some service rates, can be greater than in the initial network.

Comparison Theorems for Stochastic Chemical Reaction Networks

“…( 2010 )), on a model inspired by Braess’s paradox (see Calvert et al. ( 1997 )) and on a recently developed model describing the main interactions among histone modifications alone, and together with an expressed protein (see Bruno et al. ( 2022 )).…”

“…Now, we consider an example inspired by Braess’ paradox, which arises from transportation networks, where adding one or more roads to a road network can slow down overall traffic flow through the network (see Braess ( 1968 ) and see also a related state-dependent queuing network model in Calvert et al. ( 1997 )). A simple network of this type is one where there are two routes to get from the start to the final destination, and adding a linkage road between the routes can in some cases increase travel times.…”

Mathematical Based Models for Group Decision Support in Telecommunication Network Design and Management—Challenges and Trends

“…It was originally shown in [72] that in road transport networks (these are analog to pure delay queueing communication networks), in a non-cooperative routing approach, the bottleneck based capacity expansion may lead to a drastic increase in the delays of all users thence to a much worse network design solution -the so-called Braess paradox. An extension of this theoretical result to other networking contexts was carried out by other authors, such as [73,74], and, for loss networks, in [75,76]. [77] review this problematic and propose forms of avoiding the Braess paradoxical situation when upgrading a communication network for a general payoff function for each user (utility or cost function).…”

Avoiding paradoxes in multi-agent competitive routing

“…In a non-cooperative framework, however, this approach may have devastating effects; it may cause delays of all users to increase; in an economic context in which users pay the service provider, this may further cause a decrease in the revenues of the provider. The first problem has already been identified in road-traffic context by Braess [4] (see also [8,19]), and has further been studied in networking context in [1,3,5,7,6,12,14]. The focus of Braess paradox on the bottleneck link in a queuing context, as well as the paradoxical impact on the service provider have been studied in [16].…”