Many-server queues with customer abandonment: numerical analysis of their diffusion models

We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without service. Two diffusion models are proposed in this paper. They differ in how the patience time distribution is built into them. The first diffusion model uses the patience time density at zero and the second one uses the entire patience time distribution. To analyze these diffusion models, we develop a numerical algorithm for computing the stationary distribution of such a diffusion process. A crucial part of the algorithm is to choose an appropriate reference density. Using a conjecture on the tail behavior of a limit queue length process, we propose a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments also show that the diffusion models are good approximations for many-server queues, sometimes for queues with as few as twenty servers

Routing Games over Time with FIFO policy

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201

Network unfairness in dragonfly topologies

Dragonfly networks arrange network routers in a two-level hierarchy, providing a competitive cost-performance solution for large systems. Non-minimal adaptive routing (adaptive misrouting) is employed to fully exploit the path diversity and increase the performance under adversarial traffic patterns. Network fairness issues arise in the dragonfly for several combinations of traffic pattern, global misrouting and traffic prioritization policy. Such unfairness prevents a balanced use of the resources across the network nodes and degrades severely the performance of any application running on an affected node. This paper reviews the main causes behind network unfairness in dragonflies, including a new adversarial traffic pattern which can easily occur in actual systems and congests all the global output links of a single router. A solution for the observed unfairness is evaluated using age-based arbitration. Results show that age-based arbitration mitigates fairness issues, especially when using in-transit adaptive routing. However, when using source adaptive routing, the saturation of the new traffic pattern interferes with the mechanisms employed to detect remote congestion, and the problem grows with the network size. This makes source adaptive routing in dragonflies based on remote notifications prone to reduced performance, even when using age-based arbitration.Peer ReviewedPostprint (author's final draft

The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation