Human activity modeling and Barabasi's queueing systems

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of very low priority tasks which stay unserved almost forever as the task priority indices (PI) are "frozen in time" (i.e. a task priority is assigned once for all to each incoming task). Relaxing the "frozen in time" assumption, this paper studies the new dynamic behavior expected when the priority of each incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two class of models, namely 1) a population type model with an age structure and 2) a QS with deadlines assigned to the incoming tasks which is operated under the "earliest-deadline-first" policy, we are able to analytically extract some relevant characteristics of the the tasks waiting time distribution. As the aging mechanism ultimately assign high priority to any long waiting tasks, fat tails in the WTD cannot find their origin in the scheduling rule alone thus showing a fundamental difference between the present and the A.-L. Barabasi's class of models.Comment: 16 pages, 2 figure

Earliest-deadline-first service in heavy-traffic acyclic networks

This paper presents a heavy traffic analysis of the behavior of multi-class acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process

Modeling and Analysis of Uncertain Time-Critical Tasking Problems (UTCTP)

Modeling and Analysis of Uncertain Time-Critical Tasking Problems (UTCTP

Minimal-variance distributed scheduling under strict demands and deadlines

Many modern schedulers can dynamically adjust their service capacity to match the incoming workload. At the same time, however, variability in service capacity often incurs operational and infrastructure costs. In this abstract, we characterize an optimal distributed algorithm that minimizes service capacity variability when scheduling jobs with deadlines. Specifically, we show that Exact Scheduling minimizes service capacity variance subject to strict demand and deadline requirements under stationary Poisson arrivals. Moreover, we show how close the performance of the optimal distributed algorithm is to that of the optimal centralized algorithm by deriving a competitive-ratio-like bound

Packet Skipping and Network Coding for Delay-Sensitive Network Communication

We provide an analytical study of the impact of packet skipping and opportunistic network coding on the timely communication of messages through a single network element. In a first step, we consider a single-server queueing system with Poisson arrivals, exponential service times, and a single buffer position. Packets arriving at a network node have a fixed deadline before which they should reach the destination. To preserve server capacity, we introduce a thresholding policy, based on remaining time until deadline expiration, to decide whether to serve a packet or skip its service. The obtained goodput improvement of the system is derived, as well as the operating conditions under which thresholding can enhance performance. Subsequently, we focus our analysis on a system that supports network coding instead of thresholding. We characterize the impact of network coding at a router node on the delivery of packets associated with deadlines. We model the router node as a queueing system where packets arrive from two independent Poisson flows and undergo opportunistic coding operations. We obtain an exact expression for the goodput of the system and study the achievable gain. Finally, we provide an analytical model that considers both network coding and packet skipping, capturing their joint performance. A comparative analysis between the aforementioned approaches is provided

Second order approximation for the customer time in queue distribution under the FIFO service discipline

A single server with one customer class, serviced by the FIFO protocol, is considered and the instantaneous time in the queue profile of the customers is investigated. We provide the second order approximation for the random measure describing the customer time in the queue distribution under heavy traffic conditions

Minimal-Variance Distributed Deadline Scheduling in a Stationary Environment

Many modern schedulers can dynamically adjust their service capacity to match the incoming workload. At the same time, however, variability in service capacity often incurs operational and infrastructure costs. In this paper, we propose distributed algorithms that minimize service capacity variability when scheduling jobs with deadlines. Specifically, we show that Exact Scheduling minimizes service capacity variance subject to strict demand and deadline requirements under stationary Poisson arrivals. We also characterize the optimal distributed policies for more general settings with soft demand requirements, soft deadline requirements, or both. Additionally, we show how close the performance of the optimal distributed policy is to that of the optimal centralized policy by deriving a competitive-ratio-like bound

Heavy traffic limit for a processor sharing queue with soft deadlines

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.Comment: Published at http://dx.doi.org/10.1214/105051607000000014 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org