Computationally Efficient Simulation of Queues: The R Package queuecomputer

Large networks of queueing systems model important real-world systems such as MapReduce clusters, web-servers, hospitals, call centers and airport passenger terminals. To model such systems accurately, we must infer queueing parameters from data. Unfortunately, for many queueing networks there is no clear way to proceed with parameter inference from data. Approximate Bayesian computation could offer a straightforward way to infer parameters for such networks if we could simulate data quickly enough. We present a computationally efficient method for simulating from a very general set of queueing networks with the R package queuecomputer. Remarkable speedups of more than 2 orders of magnitude are observed relative to the popular DES packages simmer and simpy. We replicate output from these packages to validate the package. The package is modular and integrates well with the popular R package dplyr. Complex queueing networks with tandem, parallel and fork/join topologies can easily be built with these two packages together. We show how to use this package with two examples: a call center and an airport terminal.Comment: Updated for queuecomputer_0.8.

Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Methodology for modeling high performance distributed and parallel systems

Performance modeling of distributed and parallel systems is of considerable importance to the high performance computing community. To achieve high performance, proper task or process assignment and data or file allocation among processing sites is essential. This dissertation describes an elegant approach to model distributed and parallel systems, which combines the optimal static solutions for data allocation with dynamic policies for task assignment. A performance-efficient system model is developed using analytical tools and techniques. The system model is accomplished in three steps. First, the basic client-server model which allows only data transfer is evaluated. A prediction and evaluation method is developed to examine the system behavior and estimate performance measures. The method is based on known product form queueing networks. The next step extends the model so that each site of the system behaves as both client and server. A data-allocation strategy is designed at this stage which optimally assigns the data to the processing sites. The strategy is based on flow deviation technique in queueing models. The third stage considers process-migration policies. A novel on-line adaptive load-balancing algorithm is proposed which dynamically migrates processes and transfers data among different sites to minimize the job execution cost. The gradient-descent rule is used to optimize the cost function, which expresses the cost of process execution at different processing sites. The accuracy of the prediction method and the effectiveness of the analytical techniques is established by the simulations. The modeling procedure described here is general and applicable to any message-passing distributed and parallel system. The proposed techniques and tools can be easily utilized in other related areas such as networking and operating systems. This work contributes significantly towards the design of distributed and parallel systems where performance is critical

Solution methods for controlled queueing networks

In this dissertation we look at a controlled queueing network where a controller routes the incoming arrivals to parallel queues using state-dependent rules. Besides this general arrival there are dedicated arrivals to each queue. The dedicated arrivals can only be served by their designated server, hence there is no routing decision involved. The goal of the controller is to find a stationary policy that will minimize the average number of customers in the system;The problem is modeled as a semi-Markov decision process and solved using techniques from the theory of Markov decision processes. We develop an efficient policy iteration based methodology which performs better than the value iteration method which is widely thought of as the best method to use for large-scale problems. The novelty in our approach is to use iterative methods in solving the system of linear equations, and also take advantage of the sparsity of matrices. The methodology could be used for other problems that are similar in nature. Using this methodology we solve much larger problems than reported in the literature. We also look at how several heuristic methods perform on our problem. No heuristic method is suitable to use for all instances. In general, however, these heuristic methods offer quick and reasonable solutions to very large problems

Dynamic resource allocation scheme for distributed heterogeneous computer systems

This invention relates to a resource allocation in computer systems, and more particularly, to a method and associated apparatus for shortening response time and improving efficiency of a heterogeneous distributed networked computer system by reallocating the jobs queued up for busy nodes to idle, or less-busy nodes. In accordance with the algorithm (SIDA for short), the load-sharing is initiated by the server device in a manner such that extra overhead in not imposed on the system during heavily-loaded conditions. The algorithm employed in the present invention uses a dual-mode, server-initiated approach. Jobs are transferred from heavily burdened nodes (i.e., over a high threshold limit) to low burdened nodes at the initiation of the receiving node when: (1) a job finishes at a node which is burdened below a pre-established threshold level, or (2) a node is idle for a period of time as established by a wakeup timer at the node. The invention uses a combination of the local queue length and the local service rate ratio at each node as the workload indicator