Queue Policy Research Articles

ANALYSIS OF A DYNAMIC ASSIGNMENT QUEUEING MODEL WITH POISSON CLUSTER ARRIVAL PROCESSES

We consider a dynamic assignment queueing model with multiple packet classes, which has a number of queues, each with its own server. This model arises from the output buffer control of an ATM-based packet switching system, which is connected to another system via multiple links. Each packet is divided into cells and transmitted by cell-by-cell transmission through the links. Such packet arrival processes can be modeled as Poisson cluster arrival processes. An arriving packet is assigned to one of the queues according to a dynamic packet assignment scheme, which is a variation of the shortest queue policy and tries to assign buffer space and/or transmission bandwidth fairly to each class when the system is congested. We derive an approximation of the packet loss probability by using a decomposition method and an asymptotic of the cell loss probability. Its accuracy is examined in comparison with simulation results. The results of this paper can be used for dimensioning the buffer sizes of the ATM-based packet switching systems.

Approximating the mean response time of parallel queues with JSQ policy

This paper presents an accurate model for evaluating the mean system size of parallel queues with the Join the Shortest Queue (JSQ) policy. The system considered consists of N identical queues with infinite buffers, and each of the queues has one server. The job arrival process is assumed to be Poisson. The service times are assumed to be exponentially distributed. When a job arrives at the system, it is sent to the queue with the smallest number of jobs. Ties are broken by randomly selecting one of the queues with the minimal number of jobs. Exact analysis of the system is known to be very difficult, and our model gives very accurate results. A birth-death Markov process is used to model the evolution of the number of jobs in the system. An iterative procedure is devised to estimate the state transition rates. The mean job response time can then be calculated. Extensive simulations are performed and compared with the analytical results. Our results show that this method provides very accurate estimates (within 3.5%) of the mean job response times for N up to 64.

An approximate analysis of the join the shortest queue (JSQ) policy

This paper presents an accurate analytical model for evaluating the performance of the join the shortest queue (JSQ) policy. The system considered consists of N identical queues each of which may have single or multiple servers. A birth-death Markov process is used to model the evolution of the number of jobs in the system. Our results show that this method provides very accurate estimates of the average job response times.

Optimal control of multiclass parallel service systems

We consider routing and scheduling systems consisting of a number of parallel homogeneous servers with finite capacities. Assuming that jobs belong to multiple classes, we represent the interconnection of arrival streams (servers) to stations by abipartite graph, called therouting (resp.scheduling) digraph. By developing an algebraic structure on the interconnection pattern embedded in the digraph, we identify certain classes of symmetric routing and scheduling systems for which a simple control policy such as theShortest Queue policy can be shown to be optimal in the sense of optimizing the departure and loss counting processes. A counterexample is shown for systems described by digraphs with a cyclic structure.

Effect of number of packets sent simultaneously to the same output and input buffer

AbstractAn approximate numerical analysis to evaluate the mean waiting time and the blocking probability of the packet switch under first‐in/first‐out (FIFO) policy with speedup factor is performed. the improved input buffer control policy with speedup factor C is proposed to achieve small mean waiting time by computer simulation and compare the performance with conventional FIFO policy and longest queue policy. Under the proposed model, there are N/2 pairs of input buffers; if one input buffer is empty, the second packet in the queue of the other buffer is transferred to the other empty buffer. It is shown that speedup factor and proposed input buffer control policy can reduce the waiting time compared with conventional FIFO policy and longest queue policy.

Analytic modeling and comparisons of striping strategies for replicated disk arrays

Data replication has been widely used as a means of increasing the data availability for critical applications in the event of disk failure. There are different ways of organizing the two copies of the data across a disk array. This paper compares strategies for striping data of the two copies in the context of database applications. By keeping both copies active, we explore strategies that can take advantage of the additional copy to improve not only availability, but also performance during both normal and failure modes. We consider the effects of small and large stripe sizes on the performance of disk arrays with two active copies of data under a mixed workload of queries and transactions with a skewed access pattern. We propose a dual (hybrid) striping strategy which uses different stripe sizes for the two copies and a disk queuing policy designed to exploit this organization for optimal performance. An analytical model is devised for this scheme, by treating the individual disks as independent, and applying an M/G/1 queuing model. Disks on which a large query scan is running are modeled by a variation of the queue with permanent customers, which leads to an iterative functional equation for the query scan delay distribution. A solution for this equation is given. The results are validated against simulations. And are shown to match well. Comparison with uniform striping strategies show that the dual striping scheme yields the most stable performance in a variety of workloads, out-performing the uniform striping strategy using either mirrored or chained dc-clustering under both normal and failure mode operations. >

Use of application characteristics and limited preemption for run-to-completion parallel processor scheduling policies

The performance potential of run-to-completion (RTC) parallel processor scheduling policies is investigated by examining whether (1) application execution rate characteristics such as average parallelism (avg) and processor working set (PWS) and/or (2) limited preemption can be used to improve the performance of these policies. We address the first question by comparing policies (previous as well as new) that differ only in whether or not they use execution rate characteristics and by examining a wider range of the workload parameter space than previous studies. We address the second question by comparing a simple two-level queueing policy with RTC scheduling in the second level queue against RTC policies that don't allow any preemption and against dynamic equiallocation(EQ). Using simulation to estimate mean response times we find that for promising RTC policies such as adaptive static partitioning (ASP) and shortest demand first (SDF), a maximum allocation constraint that is for all practical purposes independent of avg and pws provides greater and more consistent improvement in policy performance than using avg or pws . Also, under the assumption that job demand information is unavailable to the scheduler we show that the ASP-max policy outperforms all previous high performance RTC policies for workloads with coefficient of variation in processing requirement greater than one. Furthermore, a two-level queue that allows at most one preemption per job outperforms ASP-max but is not competitive with EQ.

A Frame-Oriented Queueing Control Policy for Real- and Non-Real-Time Traffic in ATM Switches

The need to carry various real-time and non-real-time applications involving diverse traffic arrival pattern and a wide range of QoS requirements in ATM-based BISDN has spurred research activity on queueing control in ATM switches. Frame-oriented queueing policies have drawn much attention recently, which alleviates the high-speed processing requirement of the slot-oriented policies. In this paper, we propose a frame-oriented queueing control policy based on Golden-Ratio hashed slot assignment for real-time and non-real-time traffic in the output queue of ATM switches. The buffer is shared by the two types of traffic. The proposed policy updates the transmission schedule at every frame according to the buffer state instead of the arrival traffic pattern. The enqueueing priority assignment will also be updated at every frame or slot according to the transmission schedule of the current frame and the buffer state at the current frame or slot. Under the proposed policy, the minimum aggregate time-cumulative cell loss (subject to the system parameters) can always be guaranteed for any arrival traffic pattern. The system parameters need to be changed only when the traffic load and profile change (due to setup and tear-down of connections). To exploit the potential of the proposed policy, the performance of the theoretically optimal discipline R* is used to benchmark the performance of the proposed policy under a wide variety of cases.

Extremal properties of the shortest/longest non-full queue policies in finite-capacity systems with state-dependent service rates

We consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. We establish the extremal properties of the shortest non-full queue (SNQ) and the longest non-full queue (LNQ) policies, in systems with concave/convex service rates. Our analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, we solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme', in the sense of capacity balancing. Some extensions are also discussed.

Extremal properties of the shortest/longest non-full queue policies in finite-capacity systems with state-dependent service rates

We consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. We establish the extremal properties of the shortest non-full queue (SNQ) and the longest non-full queue (LNQ) policies, in systems with concave/convex service rates. Our analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, we solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme', in the sense of capacity balancing. Some extensions are also discussed.

On optimal polling policies

In a single server polling system, the server visits the queues according to a routing policy and while at a queue serves some or all of the customers there according to a service policy. A polling (or scheduling) policy is a sequence of decisions on whether to serve a customer, idle the server, or switch the server to another queue. The goal of this paper is to find polling policies that stochastically minimize the unfinished work and the number of customers in the system at all times. This optimization problem is decomposed into three subproblems: determine the optimal action (i.e., serve, switch, idle) when the server is at a nonempty queue; determine the optimal action (i.e., switch, idle) when the server empties a queue; determine the optimal routing (i.e., choice of the queue) when the server empties a queue and decides to switch. Under fairly general assumptions, we show for the first subproblem that optimal policies are greedy and exhaustive, i.e., the server should neither idle nor switch when it is at a nonempty queue. For the second subproblem, we prove that in symmetric polling systems patient policies are optimal, i.e., the server should stay idling at the last visited queue whenever the system is empty. When the system is slotted, we further prove that non-idling and impatient policies are optimal. For the third subproblem, we establish that in symmetric polling systems optimal policies belong to the class of Stochastically Largest Queue (SLQ) policies. A SLQ policy is one that never routes the server to a queue known to have a queue length that is stochastically smaller than that of another queue. This result implies, in particular, that the policy that routes the server to the queue with the largest queue length is optimal when all queue lengths are known and that the cyclic routing policy is optimal in the case that the only information available is the previous decisions.

On the Shortest Queue Policy for the Tandem Parallel Queue

We consider two nodes in tandem. At each node or service center, there are two exponential servers present with the same service rate μ and each with its own queue. Customers arrive at the first node according to a Poisson process with arrival rate λ. At their arrival, they have to be assigned to one of the servers, so they are routed to one of the queues at node 1. Customers leaving center 1 enter node 2 and are routed to one of the queues at node 2. In this paper, we consider the case with full information and the case with partial information.

Optimal queueing policies for fast packet switching of mixed traffic

The power of ATM (asynchronous transfer mode) is its ability to provide bandwidth on demand, different sources can have different bandwidth requirements. Sources also differ in performance requirements, some ask for minimal delay variations, whereas others must have extremely low cell loss probabilities. It is shown how these complementary performance requirements can be explained with an LDOLL (low delay or low loss) queue, where sources get either service priority or storage priority. The space of possible LDOLL queuing policies is very large, even after a justified reduction, the size is still O(2/sup Q2/), Q being the maximum number of ATM cells in the LDOLL queue. Using Markov decision theory and concepts of linear programming, only Q so-called efficient solutions are achieved. These are the LDOLL threshold policies, which are conceptually appealing, robust in performance, and practical from the implementation viewpoint. >

On the Optimality of the Generalized Shortest Queue Policy

Consider a queueing model in which arriving customers have to choose between m parallel servers, each with its own queue. We prove for general arrival streams that the policy which assigns to the shortest queue is stochastically optimal for models with finite buffers and batch arrivals.

Optimal Capacity Scheduling—I

Efficient algorithms are developed optimizing an important class of capacity scheduling models. The specific problem considered can be simply described in terms of contracting for warehousing capacity. Contracts must be let for warehouse capacity over n time periods, with the minimum capacity to be provided in each time period being specified. Savings may be achieved by long-term leasing arrangements or by contracting at favorable periods of time, even though this creates idle capacity at certain time periods. A minimum cost solution to this problem is sought. The mathematical model also applies to problems of equipment replacement and overhaul, checkout, repair, and replacement of stochastically failing equipment, determination of economic lot size, product assortment, and deterministic batch queuing policies, labor-force planning, and multi-commodity warehouse decisions. For some of these problems, such as equipment replacement, the computing algorithms presented are even more efficient than schemes heretofore proposed for simpler versions of the same problem.