Preemptive Priority Research Articles

Efficient exact Boolean schedulability tests for fixed priority preemption threshold scheduling

Abstract Fixed priority preemption threshold scheduling (PTS) is effective in scalable real-time system design, which requires system tuning processes, where the performance of schedulability tests for PTS matters much. This paper proposes five methods for efficient exact Boolean schedulability tests for PTS, which returns the Boolean result that tells whether the given task is schedulable or not. We regard the sufficient test for fully preemptive fixed priority scheduling (FPS) and the early exit in the response time calculations as the conventional approach. We propose (1) a new sufficient test, (2) new initial values for the start/finish times, (3) pre-calculation of the interference time within the start time, (4) incremental start/finish time calculation, and (5) early exits in start/finish time calculations. These are based on some previous work for FPS. The new initial start time, pre-calculation, and the incremental calculations also can be used for the exact response time analysis for PTS. Our empirical results show that the overall proposed methods reduce the iteration count/run time of the conventional test by about 60%/40%, regardless of the number of tasks and the total utilization.

Multi-server preemptive priority queue with general arrivals and service times

We present a simple approximate solution for preemptive-resume queues with multiple servers, general (phase-type) service and general (phase-type) interarrival time distributions. In our solution, priority levels are solved one at a time in the order of decreasing priorities. Each priority level is solved approximately using a reduced state description. The complexity of our approximate solution in terms of the number of equations solved grows linearly with the number of servers and priority levels.We studied a large number of numerical examples with a range of values for mean service times and offered loads across priority levels, varying the number of servers from 8 to 48. Discrete-event simulation was used to assess the accuracy of our approximate solution. Overall, in the case of Poisson and quasi-Poisson arrivals, expected relative error for the mean number of customers in the system was below 2% while the corresponding median relative error was below 0.25%. The good accuracy of our approximation appears to extend to the case of phase-type times between arrivals, with expected relative errors for the mean number in system below 5% even for a Pareto-like distribution of interarrival times with a large coefficient of variation. Our numerical results indicate that the proposed approximation provides a relatively simple and generally accurate approach to preemptive-resume queues with larger numbers of servers and general distributions of service and interarrival times.

Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach

Shelters are safe facilities that protect a population from possible damaging effects of a disaster. For that reason, shelter location and traffic assignment decisions should be considered simultaneously for an efficient evacuation plan. In addition, as it is very difficult to anticipate the exact place, time, and scale of a disaster, one needs to take into account the uncertainty in evacuation demand, the disruption/degradation of evacuation road network structure, and the disruption in shelters. In this study, we propose an exact algorithm based on Benders decomposition to solve a scenario-based two-stage stochastic evacuation planning model that optimally locates shelters and that assigns evacuees to shelters and routes in an efficient and fair way to minimize the expected total evacuation time. The second stage of the model is a second-order cone programming problem, and we use duality results for second-order cone programming in a Benders decomposition setting. We solve practical-size problems with up to 1,000 scenarios in moderate CPU times. We investigate methods such as employing a multicut strategy, deriving Pareto-optimal cuts, and using a preemptive priority multiobjective program to enhance the proposed algorithm. We also use a cutting plane algorithm to solve the dual subproblem since it contains a constraint for each possible path. Computational results confirm the efficiency of our algorithms.

Time-dependent analysis of an M\xa0/\xa0M\xa0/\xa0c preemptive priority system with two priority classes

We analyze the time-dependent behavior of an M / M / c priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least c high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most c - 1 high-priority customers. We then show how to compute the remaining Laplace transforms recursively, by making use of a variant of Ramaswami’s formula from the theory of M / G / 1-type Markov processes. While the primary focus of our work is on deriving Laplace transforms of transition functions, analogous results can be derived for the stationary distribution; these results seem to yield the most explicit expressions known to date.

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

AbstractA single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.

Performance analysis of cognitive radio networks for secondary users with slotted central control

This paper deals with analysis, performance evaluation and optimization of cognitive radio networks with central controller. The main principle of this technology is that secondary users are enabled to make opportunistic use of the spectrum part, which is actually unused by the primary users. The considered network enables heterogeneous slotted structure for the channel, in which the secondary user’s packets are transmitted on a slot basis, while the primary user’s packets are forwarded in super-slots, i.e. in fixed length slot-blocks. This heterogeneous slotted channel structure enables more flexible operation leading to more realistic system model of cognitive radio network. We model the cognitive radio networks by preemptive priority queueing model with two classes of customers. We solve the model by applying Markov chain technique and derive the steady-state distributions of the number of primary user’s packets and secondary user’s packets in the system. We provide the formulas for several performance measures including the interruption rate, loss rate, throughput, and average latency of secondary users. After validating the analysis by simulation the influence of the secondary user’s buffer capacity on various system performance measures is investigated. In the last part of the paper we address the question of optimal design of secondary user’s buffer capacity.

An Interactive Dynamic Fuzzy Goal Programming for Bi-level Multiobjective Linear Fractional Programming Problems.

This paper presents an interactive dynamic fuzzy goal programming (DFGP) approach for solving bi-level multiobjective linear fractional programming (BL MOLFP) problems with the characteristics of dynamic programming (DP). In the proposed approach, the membership function of the objective goals of a problem with fuzzy aspiration levels are defined first as the membership function for vector of fuzzy goals of the decision variables controlled by first–level decision maker are developed first in the model formulation of the problem. The method of variable change, on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model, is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Then, under the framework of preemptive priority based GP, a multi stage DP model of the problem is used for achievement of the highest degree (unity) of each of the membership functions. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution and the suggested algorithm to simplify the solution procedure by DP at each stage is proposed. This paper is considered as an extension work of Mahmoud A. Abo-Sinna and Ibrahim A. Baky (2010) by using dynamic approach. Finally, this approach is illustrated by a given numerical example.

Performance analysis and optimization of cognitive radio networks with retransmission control

In usual cognitive radio networks with buffer settings, secondary user packets that are interrupted by primary user packets will return to the SU buffer for later retransmission. But this may increase the average delay of the SU packets. In this paper, we propose a novel spectrum sharing strategy (SSS) to dynamically control the retransmission of the SU packets by introducing a returning threshold and a returning probability. This will simultaneously guarantee the Quality of Service for the SUs. In this SSS, when the transmission of an SU packet is interrupted, if the number of SU packets already in SU buffer reaches a returning threshold that is set in advance as a system parameter, an interrupted SU packet is admitted to return to the SU buffer with a dynamic returning probability. This returning probability is inversely proportional to the total number of packets in the system. Based on the SSS with retransmission control proposed in this paper, we build a discrete-time preemptive priority queueing model to comply with digital nature of modern networks. Accordingly, by presenting and analyzing a two-dimensional discrete-time Markov chain that represents the system state transition, we obtain the steady-state distribution of the system and then provide the formulas for several system performance measures. Moreover, with numerical results, we show the influence of the returning threshold on different performance measures. Finally, by building a net benefit function, we optimize the system performance for the returning threshold to balance different system performance measures.

Fuzzy Based Dynamic Packet Priority Determination and Queue Management method For Wireless Sensor Network

Wireless sensor networks are made up of large number of resource-constrained sensor nodes. Scheduling of different types of packets at sensor nodes is of crucial importance to reduce sensors' energy consumption, end-to-end data transmission delays and packet loss. Majority of the existing packet scheduling algorithms such as first come first serve (FCFS), preemptive priority scheduling and non-preemptive priority scheduling are not adaptive to changes in the data traffic. They also have more processing overhead and large communication delays. We propose fuzzy-based dynamic packet priority determination and queue management mechanism. In the proposed scheme, each node determines priority of packets dynamically and queues them accordingly. The proposed scheme increases fairness in scheduling and the energy efficiency by delivering the packets before their expiry. The results demonstrate that this enhanced approach outperforms FCFS and dynamic multilevel priority queue scheduling algorithms in terms of throughput, end-to-end delay and average residual energy.

Analysis of a preemptive priority retrial queue with negative customers, starting failure and at most J vacations

Analysis of a preemptive priority retrial queue with negative customers, starting failure and at most J vacations

Analysis of a preemptive priority retrial queue with negative customers, starting failure and at most J vacations

An analysis of single server preemptive priority retrial queue with at most J vacations where two types of customers called (priority customers and ordinary customers) are considered in this paper. The priority customers do not have queue and they have higher priority to receive their services over ordinary customers. If negative customer is arriving during the service time of any positive customer (priority customer or ordinary customer), it will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he may join the orbit and the priority customer will leave the system. As soon as the system is empty, the server takes at most J vacations. The probability generating functions for the system/orbit size in steady state is obtained using supplementary variable method. Some important system measures and the stochastic decomposition are discussed. Numerical examples are presented to picturise the effect of parameters on system performance measures.

Optimal revenue management in two class pre-emptive delay dependent Markovian queues

In this paper, we present a comparative study on the total revenue generated with pre-emptive and non pre-emptive priority scheduler for a fairly generic problem of pricing the server’s surplus capacity in a single server Markovian queue. The specific problem is to optimally price the server’s surplus capacity by introducing a new class of customers (secondary class) without affecting the pre-specified service level of its current customers (primary class) when pre-emption is allowed. Pre-emptive scheduling is used in various applications. First, a finite step algorithm is proposed to obtain global optimal operating and pricing parameters for this problem. These optimal operating and pricing parameters constitute a unique Nash equilibrium in a certain two player non cooperative game. We then describe the range of service level where pre-emptive scheduling gives feasible solution and generates some revenue while non pre-emptive scheduling has infeasible solution. Further, some complementary conditions are identified to compare revenue analytically for certain range of service level where strict priority to secondary class is optimal. Our computational examples show that the complementary conditions adjust in such a way that pre-emptive scheduling always generates more revenue. Theoretical analysis is found to be intractable for the range of service level when pure dynamic policy is optimal. Hence, extensive numerical examples are presented to describe different instances. It is noted in numerical examples that pre-emptive scheduling generates at least as much revenue as non pre-emptive scheduling. A certain range of service level is identified where improvement in revenue is quite significant.

Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization

In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.

Approach based on fuzzy goal programing and quality function deployment for new product planning

Quality function deployment (QFD) is a useful planning tool for facilitating new product planning (NPP) to maximize customer satisfaction. Although customer satisfaction is an important goal in NPP, other goals must also be taken into account. The evaluation of QFD involves vagueness and imprecision and thus fuzzy approaches have been applied. This study considers the satisfaction of each customer requirement (CR) as the response variable and the fulfillment levels of the corresponding design requirements (DRs) as the explanatory variables. Each CR's satisfaction expression is formulated using the mathematical programing method. Experimental design and fuzzy sets are employed to collect the input–output data set based on the evaluated relationships between CRs and DRs and the correlations among DRs in QFD processes based on the QFD team's ability, experience, and knowledge. Considering three objectives, namely the maximum customer satisfaction, minimum incremental cost and minimum technical difficulty of DRs in NPP, an additive fuzzy goal programing model is proposed to obtain the optimal satisfaction under the preemptive priority structure of all goals. Furthermore, considering that customer satisfaction complies with Herzberg's two-factor theory, this study incorporates the concept of motivation and hygiene factors into the model, to modify the fulfillment levels of DRs to enhance customer satisfaction. A numerical example is used to demonstrate the applicability of the proposed model.

Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results

In order to reduce the average delay of secondary user (SU) packets and adapt to various levels of tolerance for transmission interruption, we propose a novel opportunistic channel access mechanism with admission threshold and probabilistic feedback in cognitive radio networks (CRNs). Considering the preemptive priority of primary user (PU) packets, as well as the sensing errors of missed detection and false alarm caused by SUs, we establish a type of priority queueing model in which two classes of customers may interfere with each other. Based on this queueing model, we evaluate numerically the proposed mechanism and then present the system performance optimization. By employing a matrix-geometric solution, we derive the expressions for some important performance measures. Then, by building a reward function, we investigate the strategies for both the Nash equilibrium and the social optimization. Finally, we provide a pricing policy for SU packets to coordinate these two strategies. With numerical experiments, we verify the effectiveness of the proposed opportunistic channel access mechanism and the rationality of the proposed pricing policy.

Performance analysis of preemptive priority retrial queue with immediate Bernoulli feedback under working vacations and vacation interruption

Performance analysis of preemptive priority retrial queue with immediate Bernoulli feedback under working vacations and vacation interruption

System model and performance estimation of dynamic spectrum allocation strategy with multi-channel and imperfect sensing

ABSTRACTThe concept of cognitive radio networks (CRNs) is a promising candidate for enhancing the utilization of existing radio spectrum. In CRNs, secondary users (SUs) are allowed to use the spectrum unused by primary users (PUs). In order to mathematically estimate the system performance of dynamic spectrum allocation strategy with multi-channel and imperfect sensing, we propose a novel preemptive priority queueing model. We establish a discrete-time Markov chain in line with the stochastic behaviour of SU and PU packets. Then, we derive some performance measures, such as the interference rate of PU packets, the normal throughput and the average delay of SU packets. Moreover, we provide theoretical and simulation experiments to investigate the system performance. Numerical experiments show that there is a tradeoff between different performance measures when imperfect sensing is considered. Finally, we present an optimal design for setting the number of the channels in a spectrum.

Energy-saving strategy for green cognitive radio networks with an LTE-advanced structure

A green cognitive radio network (CRN), characterized by base stations (BSs) that conserve energy during sleep periods, is a promising candidate for realizing more efficient spectrum allocation. To improve the spectrum efficiency and achieve greener communication in wireless applications, we consider CRNs with an long term evolution advanced (LTE-A) structure and propose a novel energy-saving strategy. By establishing a type of preemptive priority queueing model with a single vacation, we capture the stochastic behavior of the proposed strategy. Using the method of matrix geometric solutions, we derive the performance measures in terms of the average latency of secondary user (SU) packets and the energy-saving degree of BSs. Furthermore, we provide numerical results to demonstrate the influence of the sleeping parameter on the system performance. Finally, we compare the Nash equilibrium behavior and social optimization behavior of the proposed strategy to present a pricing policy for SU packets.

On a general mixed priority queue with server discretion

ABSTRACTWe consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.

Dynamic Pricing of Preemptive Service for Secondary Demand

Motivated by recent regulatory evolutions that pave the way to secondary spectrum markets, we investigate profit maximization in a loss network that accommodates calls of two classes of users: 1) primary users (PUs) and 2) secondary users (SUs). PUs have preemptive priority over SUs, i.e., when a PU arrives to the system and finds all channels busy, it preempts an SU. We assume that SU demand is sensitive to price whereas PU demand is inelastic. We study the optimal pricing policy of SUs to maximize the average profit by introducing a finite horizon discounted dynamic programming formulation. Our main contribution is to show that the optimal pricing policy depends only on the total number of users, i.e., the total occupancy. We also demonstrate that optimal prices increase with the total occupancy and show that the optimal pricing policy structure of the original system is not preserved for systems with price-sensitive PUs. Finally, we extend the results to non-preemptive loss systems and establish a connection with results obtained for such models in the literature.