A Fluid-Diffusion-Hybrid Limiting Approximation for Priority Systems with Fast and Slow Customers

2021 ◽  
Author(s):  
Lun Yu ◽  
Seyed Iravani ◽  
Ohad Perry
Keyword(s):  
Heavy Traffic ◽  
Priority Queue ◽  
Costs And Benefits ◽  
Fluid Limit ◽  
Asymptotically Optimal ◽  
Asymptotic Regime ◽  
Limit Process ◽  
Priority Systems ◽  
Pool System ◽  
Fluid Diffusion

The paper “Fluid-Diffusion-Hybrid (FDH) Approximation” proposes a new heavy-traffic asymptotic regime for a two-class priority system in which the high-priority customers require substantially larger service times than the low-priority customers. In the FDH limit, the high-priority queue is a diffusion, whereas the low-priority queue operates as a (random) fluid limit, whose dynamics are driven by the former diffusion. A characterizing property of our limit process is that, unlike other asymptotic regimes, a non-negligible proportion of the customers from both classes must wait for service. This property allows us to study the costs and benefits of de-pooling, and prove that a two-pool system is often the asymptotically optimal design of the system.

scholarly journals Laws of Little in an open queueing network

2012 ◽  
Vol 17 (3) ◽  
pp. 327-342 ◽  
Author(s):  
Saulius Minkevičius ◽  
Stasys Steišūnas
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Queue Length ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Large Numbers ◽  
Virtual Waiting Time ◽  
Open Queueing Network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented.

Exponential spectra as a tool for the study of server-systems with several classes of customers

1978 ◽  
Vol 15 (01) ◽  
pp. 162-170 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Heavy Traffic ◽  
Transient Behavior ◽  
Single Server ◽  
Idle State ◽  
Priority Systems ◽  
Completely Monotone ◽  
Server Systems ◽  
Server System

For a single-server system having several Poisson streams of customers with exponentially distributed service times, busy period densities, waiting time densities, and idle state probabilities are completely monotone. The exponential spectra for such densities are of importance for understanding the transient behavior of such systems. Algorithms are given for the computation of such spectra. Applications to heavy traffic situations and priority systems are also discussed.

Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks

1995 ◽  
Vol 27 (01) ◽  
pp. 273-292 ◽  
Author(s):  
N. G. Bean ◽  
R. J. Gibbens ◽  
S. Zachary
Keyword(s):  
Asymptotic Analysis ◽  
Wide Class ◽  
Heavy Traffic ◽  
Resource Loss ◽  
Call Blocking ◽  
Integrated Networks ◽  
Asymptotic Regime ◽  
Finite Systems ◽  
Empirical Results ◽  
Loss Systems

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis. methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples.

scholarly journals HYDRODYNAMIC LIMIT OF ORDER-BOOK DYNAMICS

2016 ◽  
Vol 32 (1) ◽  
pp. 96-125 ◽  
Author(s):  
Xuefeng Gao ◽  
S.J. Deng
Keyword(s):  
Hydrodynamic Limit ◽  
Order Book ◽  
Fluid Limit ◽  
Fluid Approximation ◽  
Asymptotic Regime ◽  
Empirical Results ◽  
Time Periods ◽  
Good For

In this paper, we establish a fluid limit for a two-sided Markov order book model. The main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the “sell-side shape” and “buy-side shape” of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test the fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly traded stocks in certain time periods.

scholarly journals Nudge: Stochastically Improving upon FCFS

2021 ◽  
Vol 5 (2) ◽  
pp. 1-29
Author(s):  
Isaac Grosof ◽  
Kunhe Yang ◽  
Ziv Scully ◽  
Mor Harchol-Balter
Keyword(s):  
Response Time ◽  
Open Problem ◽  
Scheduling Algorithm ◽  
Size Distributions ◽  
Asymptotically Optimal ◽  
Asymptotic Regime ◽  
Scheduling Policy ◽  
Asymptotic Tail

The First-Come First-Served (FCFS) scheduling policy is the most popular scheduling algorithm used in practice. Furthermore, its usage is theoretically validated: for light-tailed job size distributions, FCFS has weakly optimal asymptotic tail of response time. But what if we don't just care about the asymptotic tail? What if we also care about the 99th percentile of response time, or the fraction of jobs that complete in under one second? Is FCFS still best? Outside of the asymptotic regime, only loose bounds on the tail of FCFS are known, and optimality is completely open. In this paper, we introduce a new policy, Nudge, which is the first policy to provably stochastically improve upon FCFS. We prove that Nudge simultaneously improves upon FCFS at every point along the tail, for light-tailed job size distributions. As a result, Nudge outperforms FCFS for every moment and every percentile of response time. Moreover, Nudge provides a multiplicative improvement over FCFS in the asymptotic tail. This resolves a long-standing open problem by showing that, counter to previous conjecture, FCFS is not strongly asymptotically optimal.

Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks

1995 ◽  
Vol 27 (1) ◽  
pp. 273-292 ◽  
Author(s):  
N. G. Bean ◽  
R. J. Gibbens ◽  
S. Zachary
Keyword(s):  
Asymptotic Analysis ◽  
Wide Class ◽  
Heavy Traffic ◽  
Resource Loss ◽  
Call Blocking ◽  
Integrated Networks ◽  
Asymptotic Regime ◽  
Finite Systems ◽  
Empirical Results ◽  
Loss Systems

In this paper we consider the analysis of call blocking at a single resource with differing capacity requirements as well as differing arrival rates and holding times. We include in our analysis trunk reservation parameters which provide an important mechanism for tuning the relative call blockings to desired levels. We base our work on an asymptotic regime where the resource is in heavy traffic. We further derive, from our asymptotic analysis. methods for the analysis of finite systems. Empirical results suggest that these methods perform well for a wide class of examples.

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