Fixed-priority Policy Research Articles

The Generalized c/μ Rule for Queues with Heterogeneous Server Pools

Dynamic Routing of Queues with Heterogeneous Server Pools In “The Generalized c/μ Rule for Queues with Heterogeneous Server Pools,” Long, Zhang, Zhang, and Zhang study the optimal control of queueing systems with heterogeneous server pools and a single customer class. The goal is to balance the holding cost of the queue with the operating costs of the server pools. They introduce the target-allocation policy, the Gc/μ rule, and the fixed priority policy for systems with general, convex, and concave cost functions, respectively. They also consider an extension to minimize operating costs and maintain a service-level target for customers waiting in the queue. Moreover, they show that their asymptotically optimal routing policies coincide with several classic policies in the literature in special cases.

Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

For a queueing system with multiple customer types differing in service-time distributions and waiting costs, it is well known that the cµ-rule is optimal if costs for waiting are incurred linearly with time. In this paper, we seek to identify policies that minimize the long-run average cost under nonlinear waiting cost functions within the set of fixed priority policies that only use the type identities of customers independently of the system state. For a single-server queueing system with Poisson arrivals and two or more customer types, we first show that some form of the cµ-rule holds with the caveat that the indices are complex, depending on the arrival rate, higher moments of service time, and proportions of customer types. Under quadratic cost functions, we provide a set of conditions that determine whether to give priority to one type over the other or not to give priority but serve them according to first-come, first-served (FCFS). These conditions lead to useful insights into when strict (and fixed) priority policies should be preferred over FCFS and when they should be avoided. For example, we find that, when traffic is heavy, service times are highly variable, and the customer types are not heterogenous, so then prioritizing one type over the other (especially a proportionally dominant type) would be worse than not assigning any priority. By means of a numerical study, we generate further insights into more specific conditions under which fixed priority policies can be considered as an alternative to FCFS. This paper was accepted by Baris Ata, stochastic models and simulation.

Pessimism in multicore global schedulability analysis

Abstract When it comes to multicore real-time systems, the global scheduling that allows tasks to migrate between different cores and the partitioned scheduling that statically allocates tasks to individual cores are two popular policies. However, due to the complexity and pessimism of multicore schedulability tests, there is no simple way to compare the effectiveness of global versus partitioned scheduling, and it is hard to improve existing analysis methods. In this paper, we formally prove that, according to state-of-the-art global schedulability tests, if a multicore task system (with Di ≤ Ti) is deemed schedulable under global fixed priority policy, we can easily find a schedulable partitioning for it too. This result holds also for self-suspending tasks that can suspend its own execution voluntarily. Such a fact reveals the high pessimism in current global schedulability tests. To tackle this, we propose a 2-part execution scenario, by simply considering the task execution into two parts, that helps better estimate the interference a task suffers. Using this method, a new global schedulability test can detect schedulable tasksets that will be non-schedulable by any partitioned scheduling algorithm. Our proposed method indicates a new direction for designing global schedulability tests. In the experiments, comparisons with other global and partitioned schedulability tests confirm the improvement by using our new test.

Ergodic control of multi-class $M/M/N+M$ queues in the Halfin–Whitt regime

We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin–Whitt (QED) regime, that is, the number of servers $n$ and the total offered load $\mathbf{r}$ scale like $n\approx\mathbf{r}+\hat{\rho}\sqrt{\mathbf{r}}$ for some constant $\hat{\rho}$. This problem was proposed in [Ann. Appl. Probab. 14 (2004) 1084–1134, Section 5.2]. The optimal solution of this control problem can be approximated by that of the corresponding ergodic diffusion control problem in the limit. We introduce a broad class of ergodic control problems for controlled diffusions, which includes a large class of queueing models in the diffusion approximation, and establish a complete characterization of optimality via the study of the associated HJB equation. We also prove the asymptotic convergence of the values for the multi-class queueing control problem to the value of the associated ergodic diffusion control problem. The proof relies on an approximation method by spatial truncation for the ergodic control of diffusion processes, where the Markov policies follow a fixed priority policy outside a fixed compact set.

On the risk-sensitive cost for a Markovian multiclass queue with priority

A multi-class M/M/1 system, with service rate $\mu_in$ for class-$i$ customers, is considered with the risk-sensitive cost criterion $n^{-1}\log E\exp\sum_ic_iX^n_i(T)$, where $c_i>0$, $T>0$ are constants, and $X^n_i(t)$ denotes the class-$i$ queue-length at time $t$, assuming the system starts empty. An asymptotic upper bound (as $n\to\infty$) on the performance under a fixed priority policy is attained, implying that the policy is asymptotically optimal when $c_i$ are sufficiently large. The analysis is based on the study of an underlying differential game.

Feasibility analysis of real-time transactions

The objective of this paper is two-fold: give a survey of response time analysis (RTA), and contribute to schedulability analysis for the real-time transaction model. The RTA is studied under fixed priority policies (FPP), while schedulability analysis assumes an optimal scheduling algorithm (like the deadline driven scheduling algorithm EDF) in a preemptive context on uniprocessor systems. We compare the transaction model to the family of multiframe models, then present the exact, and approximated methods, as well as a tunable method to compute the RTA. Finally we present a new schedulability analysis method and an efficient algorithm to speed up this test.

Applying global time Petri net analysis on the embedded software context

This paper presents an application of Global Time technique (GTT) which is an approach to construct class graphs of Time Petri nets based on relative and global time. Besides the constructing of GTT class graph we propose a schedulability analysis of quantitative time type for fixed priority policies and Earliest Deadline First (EDF). We propose that analysis of scenarios, or behavior itineraries duration of a system, can be done using this approach.

Durée exacte de montée en charge des systèmes temps-réel par une politique à priorités fixes. Périodiques ordonnancés en multiprocesseur

We consider periodic task systems scheduled under a fixed priority policy on a multiprocessor platform. First, we determine the time needed to reach the cyclic behavior. Next, we deduce several upper bounds with reduced computational complexities in comparison with exact computation. Finally, these bounds are evaluated through numerical experimentations.