Variance Of Waiting Time Research Articles

Activity Scheduling on Identical Parallel Processors

The efficiency of parallel processors is achieved for the purpose of quick computing is mainly depending on the scheduling of activity. The most important factor for scheduling of activities are depend on the waiting time which is directly influence the computation time of overall activity. Minimizing the Variance of Waiting Time otherwise known as Waiting Time Variance (WTV) is one of the metrics of Quality of Services (QoS) which enhance the efficiency of activity scheduling. Allocate the activity from a set of activity pool and schedule them for each identical parallel processor for execution in a large scale by minimizing WTV is the main focusing area of this paper. In case of large scale computing activities are complex in nature. A prior knowledge of each activity must be known before the preparation of activity scheduling for efficient and rapid computing. A snake walks style of activity distribution among the parallel processor is presented in this paper for minimization problem. The minimization of WTV is measured with the help of three heuristic intend methods named as RSS, VS and BS. The results of the experiment are compared with current conspires and demonstrate the new snake style conspire is presenting the best practices for proven conspires and challenges in a wide range of activity. The algorithm's predictable findings appear as illustrated with graph.

Sustainable Queuing-Network Design for Airport Security Based on the Monte Carlo Method

The design of airport queuing networks is a significant research field currently for researchers. Many factors must to be considered in order to achieve the optimized strategies, including the passenger flow volume, boarding time, and boarding order of passengers. Optimizing these factors lead to the sustainable development of the queuing network, which currently faces a few difficulties. In particular, the high variance in checkpoint lines can be extremely costly to passengers as they arrive unduly early or possibly miss their scheduled flights. In this article, the Monte Carlo method is used to design the queuing network so as to achieve sustainable development. Thereafter, a network diagram is used to determine the critical working point, and design a structurally and functionally sustainable network. Finally, a case study for a sustainable queuing-network design in the airport is conducted to verify the efficiency of the proposed model. Specifically, three sustainable queuing-network design solutions are proposed, all of which not only maintain the same standards of security, but also increase checkpoint throughput and reduce passenger waiting time variance.

Discrete-time bulk service queuing processes.

In this paper an analysis of bulk service queuing system of Bailey and Jaiswal is made considering time as a discrete variable. Expressions for Average and Variance of queue length and average waiting-time are obtained when the input distribution is binomial and service-time is identically and independently distributed. The results of Bailey and Torben Meisling are shown as particular cases. These results are applied to find the Mean and Variance of queue length and mean waiting time in the special cases (i) when the service-time is constant and (ii) when the service-time follows geometric distribution.

Simultaneous minimization of total tardiness and waiting time variance on a single machine by genetic algorithms

This paper considers a single machine scheduling problem, with the objective of minimizing a linear combination of total tardiness and waiting time variance in which the idle time is not allowed. Minimizing total tardiness is always regarded as one of the most significant performance criteria in practical systems to avoid penalty costs of tardiness, and waiting time variance is an important criterion in establishing quality of service (QoS) in many systems. Each of these criteria is known to be non-deterministic polynomial-time hard (NP-hard); therefore, the linear combination of them is NP-hard too. For this problem, we developed a genetic algorithm (GA) by applying its general structure that further improves the initial population, utilizing some of heuristic algorithms. The GA is shown experimentally to perform well by testing on various instances.

Minimizing weighted waiting time variance on a single processor

This paper considers the problem of scheduling n non-preemptive jobs on a single processor. Each job may have different size and weight. The objective is to minimize the weighted waiting time variance (WWTV). It is shown that the proof of one previous established optimality property in the literature, called “agreeably weighted property”, is wrong and the corrected proof is presented. Additional optimality properties are proved for the cases where job sizes are directly or inversely proportional to their weights, respectively. In addition, we show that the objective function of the problem can be expressed as a function of positional weights and processing times. With this new functional form, the proofs of several previously established optimality properties in the literature become rather straightforward.

Applications of machine learning approach on multi-queue message scheduling

Due to limited resource contentions and deadline constraints, messages on the controller area network (CAN) are competing for service from the common resources. This problem can be resolved by assigning priorities to different message classes to satisfy time-critical applications. Actually, because of the fluctuation of network traffic or an inefficient use of resources, these static or dynamic priority policies may not guarantee flexibility for different kinds of messages in real-time scheduling. Consequently, the message transmission which cannot comply with the timing requirements or deadlines may deteriorate system performance significantly. In this paper, we have proposed a controller-plant model, where the plant is analogous to a message queue pool (MQP) and the message scheduling controller (MSC) is responsible to dispatch resources for queued messages according to the feedback information from the MQP. The message scheduling controller, which is realized by the radial basis function (RBF) network, is designed with machine learning algorithm to compensate the variations in plant dynamics. The MSC with the novel hybrid learning schemes can ensure a low and stable message waiting time variance (or a uniform distribution of waiting time) and lower transmission failures. A significant emphasis of the MSC is the variable structure of the RBF model to accommodate to complex scheduling situations. Simulation experiments have shown that several variants of the MSC significantly improve overall system performance over the static scheduling strategies and the dynamic earliest-deadline first (EDF) algorithms under a wide range of workload characteristics and execution environments.

An Evolutionary Hybrid Scheduling Algorithm for Computational Grids

Grids promote user collaboration through flexible, coordinated sharing of distributed resources to solve a single large problem. Grid scheduling, similar to resource discovery and monitoring, is inherently more complex in Grid environments. We propose two approaches for solving Grid scheduling problems with the simultaneous objectives of maximizing the number of workflow executions and minimizing the waiting time variance among tasks of each workflow. One is the multiple objective Niched Pareto Genetic Algorithm (NPGA) that involves evolution during a comprehensive search and work on multiple solutions. After the Genetic search, we strengthen the search using Simulated Annealing as a local search meta-heuristic. For comparison, we evaluate other scheduling, such as, Tabu Search (TS), Simulated annealing (SA), and Discrete Particle Swarm Optimization (Discrete PSO). Results show that our proposed evolutionary Hybrid scheduling involving NPGA with an SA search, works better than other scheduling in considering workflow execution time within a deadline and waiting time variance in tasks with minimal iterations.

Minimization of Job Waiting Time Variance on Identical Parallel Machines

We consider the problem of scheduling independent jobs on identical parallel machines so as to minimize the waiting time variance of the jobs ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ). We show that the optimal value of( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) is identical to the optimal value of the problem for minimizing the completion time variance of jobs on identical parallel machines( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ). We prove that, given the same job set, any feasible schedule of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) can be transformed into the feasible solution for ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) with the same job set by applying the polynomial algorithms proposed in this paper. Several other important properties of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) are also proved. Heuristic algorithms are proposed to solve ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) problems. We present the testing results of these heuristic algorithms, which are applied to problems with both small and large job sets.

Influencing factors of job waiting time variance on a single machine

When a batch of jobs are waiting for services from a machine or resource, sometimes it is desirable to minimise the variance of job waiting times Waiting Time Variance (WTV) for service stability to all the jobs in the batch so that the jobs have about the same waiting times. Many factors, including the sum of the jobs' processing times, the probability distribution of job processing times and the scheduling method may influence the variance of job waiting times. In this paper, we use multivariate exploratory techniques such as Principal Components Analysis (PCA) and Correspondence Analysis (CA) along with other statistical analysis techniques to investigate these factors. We prove that the expected WTV can be predicted given characteristics of the jobs. These findings can be applied to achieve a desire level of WTV for service stability.

Job scheduling to minimize the weighted waiting time variance of jobs

This study considers the job scheduling problem of minimizing the weighted waiting time variance (WWTV) of jobs. It is an extension of WTV minimization problems in which we schedule a batch of n jobs, for servicing on a single resource, in such a way that the variance of their waiting times is minimized. WWTV minimization finds its applications for job scheduling in manufacturing systems with earliness and tardiness (E/T) penalties, in computer and networks systems for the stabilized QoS, and in other fields where it is desirable to minimize WWTV of jobs with different weights for priorities. We formulate a WWTV problem as an integer programming problem, prove the V-shape property for agreeably weighted WWTV problems and the nondelay property for general WWTV problems, and discover the strong V-Shape tendency of the optimal job sequences for this problem. Two job scheduling algorithms, Weighted Verified Spiral (WVS) and Weighted Simplified Spiral (WSS), are developed for the WWTV problems. Numerical testing shows that WVS and WSS significantly outperform existing WWTV algorithms.

Job scheduling methods for reducing waiting time variance

Minimizing Waiting Time Variance (WTV) is a job scheduling problem where we schedule a batch of n jobs, for servicing on a single resource, in such a way that the variance of their waiting times is minimized. Minimizing WTV is a well known scheduling problem, important in providing Quality of Service (QoS) in many industries. Minimizing the variance of job waiting times on computer networks can lead to stable and predictable network performance. Since the WTV minimization problem is NP-hard, we develop two heuristic job scheduling methods, called Balanced Spiral and Verified Spiral, which incorporate certain proven properties of optimal job sequences for this problem. We test and compare our methods with four other job scheduling methods on both small and large size problem instances. Performance results show that Verified Spiral gives the best performance for the scheduling methods and problems tested in this study. Balanced Spiral produces comparable results, but at less computational cost. During our investigation we discovered a consistent pattern in the plot of WTV over mean of all possible sequences for a set of jobs, which can be used to evaluate the sacrifice of mean waiting time while pursuing WTV minimization.

Variance Minimization – Relationship between Completion-Time Variance and Waiting-Time Variance

AbstractThe completion-time variance (CTV) and the waiting-time variance (WTV) are two performance measures which are commonly used in optimization of single-machine scheduling systems. This paper shows that when the number of jobs is large the two measures are nearly equivalent in a probabilistic environment.

The effect of routeing and machine flexibility on the performance of manufacturing systems

Abstract The effect of routeing and machine flexibility on the performance of manufacturing systems is investigated. The results obtained indicate that in a variable environment, a positive correlation between flexibility and several measures of performance may indeed exist. These measures include part mean flow time and waiting time, flow time and waiting time variance, and mean and variance of work-in-process inventory. The significance of the effect of routeing and machine flexibility is shown to increase with increases in either the degree of variability in the system or in the level of system loading. In addition, the relationship between flexibility and performance is found to be of the diminishing return type. That is, most of the performance improvements are achieved at relatively low levels of flexibility. It is also shown that the effect of part flow control policies (e.g. dispatching rules) diminishes with increases in routeing and machine flexibility. The benefits of flexibility are found, how...

Distributed round-robin and first-come first-serve protocols and their applications to multiprocessor bus arbitration

Two new distributed protocols for fair and efficient bus arbitration are presented. The protocols implement round-robin (RR) and first-come first-serve (FCFS) scheduling, respectively. Both protocols use relatively few control lines on the bus, and their logic is simple. The round-robin protocol, which uses statically assigned arbitration numbers to resolve conflict during an arbitration, is more robust and simpler to implement than previous distributed RR protocols that are based on rotating agent priorities. The proposed FCFS protocol uses partly static arbitration numbers, and is the first practical proposal for a FCFS arbiter known to the authors. The proposed protocols thus have a better combination of efficiency, cost, and fairness characteristics than existing multiprocessor bus arbitration algorithms. Three implementations of our RR protocol, and two implementations of our FCFS protocol, are discussed. Simulation results are presented that address: 1) the practical potential for unfairness in the simpler implementation of the FCFS protocol, 2) the practical implications of the higher waiting time variance in the RR protocol, and 3) the allocation of bus bandwidth among agents with unequal request rates in each protocol. The simulation results indicate that there is very little practical difference in the performance of the two protocols.

The serial correlation coefficients of waiting times in a stationary single server queue

SummaryIn a stationaryGI/G/1 queueing system in which the waiting time variance is finite, it can be shown that the serial correlation coefficients {ρn} of a (stationary) sequence of waiting times are non-negative and decrease monotonically to zero. By means of renewal theory we find a representation for Σ∞0ρnfrom which necessary and sufficient condition for its finiteness can be found. InM/G/1 rather more can be said: {ρn} is convex sequence, the asymptotic form of ρncan be given in a nearly saturated queue, and a simple explicit expression for Σ∞0ρnexists. For the stationaryM/M/1queue we find the ρn's explicitly, illustrate them numerically, and derive a representation which shows that {ρn} is completely monotonic.

Time Dependent Priority Queues

Considered is a class of rth order delay-dependent priority queuing disciplines in which a customer from the pth priority group, who arrives at time T, has a priority qp(t) at time t given by qp(t) = bp(t − T)r. The main result states that the expected wait on queue for p-type customers in an rth order system with parameter set [bp] is identical to the wait in any other such system, say one of order r′ with parameter set [bp′] if these parameters are chosen in the proper manner. From this, using the results due to Kleinrock for the first order systems, we obtain the expected wait on queue, conditioned on the priority groups, for any rth order system. This class of queuing disciplines ranges from Cobham's fixed priority system (for r → 0) to the first-come-first-served system (for r → ∞). For the case of two priority groups the set {bp} is chosen so as to minimize a class of delay-dependent cost functions. Results from a computer simulation are given to display the behavior of the waiting time variance.

The effect of queue discipline on waiting time variance

It is usual in the theory of queues to assume that customers are served in the order of their arrival. In some applications (e.g. telephone engineering), however, other forms of queue discipline are more realistic. The precise effect of any such change on the waiting-time distribution of a customer will depend on the procedure envisaged (random service, “last come, first served”, etc.), but it is possible to make certain general statements. Thus it is well known that, under certain conditions, the mean is independent of the queue discipline. The purpose of the present note is to consider the variance of waiting time, and we shall prove that this is a minimum when the customers are served in order of arrival. Thus this is, in a sense, the “fairest” queue discipline. This does not, of course, mean that other procedures may not be justified when different criteria are taken into account.