Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data

Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application

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.

Maximum likelihood estimation of closed queueing network demands from queue length data

We propose maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent stations. Our ML estimators are expressed in implicit form and require only to compute mean queue lengths and marginal queue length probabilities from an empirical dataset. Further, in the load-independent case, we provide an explicit approximate formula for the ML estimator together with confidence intervals

The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

Bayesian inference for queueing networks and modeling of internet services

Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. Such services are modeled by networks of queues, where each queue models one of the computers in the system. A key challenge is that the data are incomplete, because recording detailed information about every request to a heavily used system can require unacceptable overhead. In this paper we develop a Bayesian perspective on queueing models in which the arrival and departure times that are not observed are treated as latent variables. Underlying this viewpoint is the observation that a queueing model defines a deterministic transformation between the data and a set of independent variables called the service times. With this viewpoint in hand, we sample from the posterior distribution over missing data and model parameters using Markov chain Monte Carlo. We evaluate our framework on data from a benchmark Web application. We also present a simple technique for selection among nested queueing models. We are unaware of any previous work that considers inference in networks of queues in the presence of missing data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS392 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cloud Enabled Emergency Navigation Using Faster-than-real-time Simulation

State-of-the-art emergency navigation approaches are designed to evacuate civilians during a disaster based on real-time decisions using a pre-defined algorithm and live sensory data. Hence, casualties caused by the poor decisions and guidance are only apparent at the end of the evacuation process and cannot then be remedied. Previous research shows that the performance of routing algorithms for evacuation purposes are sensitive to the initial distribution of evacuees, the occupancy levels, the type of disaster and its as well its locations. Thus an algorithm that performs well in one scenario may achieve bad results in another scenario. This problem is especially serious in heuristic-based routing algorithms for evacuees where results are affected by the choice of certain parameters. Therefore, this paper proposes a simulation-based evacuee routing algorithm that optimises evacuation by making use of the high computational power of cloud servers. Rather than guiding evacuees with a predetermined routing algorithm, a robust Cognitive Packet Network based algorithm is first evaluated via a cloud-based simulator in a faster-than-real-time manner, and any "simulated casualties" are then re-routed using a variant of Dijkstra's algorithm to obtain new safe paths for them to exits. This approach can be iterated as long as corrective action is still possible.Comment: Submitted to PerNEM'15 for revie