Separation of timescales in a two-layered network

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traffic: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a fixed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.Comment: 8 pages, 2 figures, 1 table, ITC 24 (2012

Fluid Models of Many-server Queues with Abandonment

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide first-order approximation for this model. The fluid model solution, which is proved to uniquely exists, serves as the fluid limit of the many-server queue, as the number of servers becomes large. Based on the fluid model solution, first-order approximations for various performance quantities are proposed

Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment

Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable approximations to the steady state of the original stochastic systems. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under a mild condition. Our method builds on the framework of measure-valued processes developed in Zhang (2013), which keeps track of the remaining patience and service times

On the stability of flow-aware CSMA

We consider a wireless network where each flow (instead of each link) runs its own CSMA (Carrier Sense Multiple Access) algorithm. Specifically, each flow attempts to access the radio channel after some random time and transmits a packet if the channel is sensed idle. We prove that, unlike the standard CSMA algorithm, this simple distributed access scheme is optimal in the sense that the network is stable for all traffic intensities in the capacity region of the network

Upstream traffic capacity of a WDM EPON under online GATE-driven scheduling

Passive optical networks are increasingly used for access to the Internet and it is important to understand the performance of future long-reach, multi-channel variants. In this paper we discuss requirements on the dynamic bandwidth allocation (DBA) algorithm used to manage the upstream resource in a WDM EPON and propose a simple novel DBA algorithm that is considerably more efficient than classical approaches. We demonstrate that the algorithm emulates a multi-server polling system and derive capacity formulas that are valid for general traffic processes. We evaluate delay performance by simulation demonstrating the superiority of the proposed scheduler. The proposed scheduler offers considerable flexibility and is particularly efficient in long-reach access networks where propagation times are high