510739
An analysis of queueing systems with multi-task servers
Abstract We study a Markovian queueing system with multi-task servers. Each server can perform two types of job-serving the queue as primary jobs and taking vacations as secondary jobs. In such a system with c>1 servers, if at a service completion instant the server finds no customer waiting in line and the number of servers already on vacations is less than d(⩽c), he or she will take a vacation. At any time, the number of servers attending the queue or staying idle is at least c−d. By changing the parameter d, the queueing manager can better allocate the servers’ time to performing the primary jobs and the secondary jobs. Using the matrix analytic method, we provide a new computational algorithm for the stationary distributions of the queue length and waiting time. The conditional stochastic decomposition properties have been established for such a system.
5191709
Discrete Time Geo/G/1 Queue with Multiple Adaptive Vacations
This paper treats the discrete time Geometric/G/1 system with vacations. In this system, after serving all customers in the system, the server will take a random maximum number of vacations before returning to the service mode. The stochastic decomposition property of steady-state queue length and waiting time has been proven. The busy period, vacation mode period, and service mode period distributions are also derived. Several common vacation policies are special cases of the vacation policy presented in this study.
1280703
Stationary Distributions of GI/M/c Queue with PH Type Vacations
We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.
20091556
Allocating kanbans for a production system in a general configuration with a new control strategy
We consider a production system in a general configuration with a new control strategy: the push policy for the part sending and the kanban mechanism for the work-in-process (WIP). The production system is composed of many stations (or workshops) such as an entry station, a set of workstations, a central station, and an exit station. This type of system is modeled as an open queueing network (OQN) in a general configuration with a Markov-type part sending policy and a machine no blocking (MNB) mechanism. The most important performance measures of the production system are the total throughput of the workstations and the total blocking flow of blocked parts sent from the workstations to the central station. This paper discusses an optimization problem with multiple objectives: allocate kanbans to the workstations so as to simultaneously maximize the total throughput and minimize the total blocking flow. Based on a semi-open decomposition approach, several useful properties of the system are characterized. These properties are used to develop a marginal algorithm for the optimization problem. Moreover, a dynamic simulation approach is devised as a tool for evaluating the quality of the solutions obtained by the algorithm. Numerical experiments are provided to demonstrate the efficiency of the algorithm through the simulation approach.
41203874
Optimal Two-Threshold Policies in an M/G/1 Queue With Two Vacation Types
This paper treats two-threshold policies for an M/G/1 queue with two types of generally distributed random vacations: type 1 (long) and type 2 (short) vacations. Upon returning from a vacation, the server observes the queue length. If this is less than the lower threshold, the server takes a type 1 vacation; if it is between the two thresholds, the server takes a type 2 vacation; and if it is at or above the upper threshold, the server resumes serving the queue exhaustively. There is a shutdown cost for starting a series of vacations, a linear customer waiting cost, and type-dependent vacation reward rates. Renewal theory or the PASTA property is used to develop expressions for the average queue length and the average system cost for generally distributed vacations. A search procedure, which is provably finite for exponentially distributed vacations, is developed for determining the optimal threshold values.
45941410
The optimal service time allocation of a versatile server to queue jobs and stochastically available non-queue jobs of different types
Abstract In this paper, we consider a service system in which the server can process N + 1 different types of jobs. Jobs of type 0 are generated randomly according to a Poisson stream. Jobs of types 1 to N are non-queue types which may or may not be available for completion by the server. To optimally allocate the server's time to these jobs, we formulate a finite state semi-Markov decision process model to this environment. With this model, the optimal stationary policies can be numerically determined via a policy-iteration algorithm. We also discuss the practical applications of this model to tele-service and tele-marketing operations.
2737366
A proof of an inequality concerning k-restricted edge connectivity
An edge subset S of a connected graph G is a k-restricted edge cut if G-S is disconnected, and every component of G-S has at least k vertices. The k-restricted edge connectivity is the cardinality of a minimum k-restricted edge cut. In this note, we show that except for a well-defined class of graphs, k-restricted edge cuts of a connected graph G exist for any k=<@d(G)+1, where @d(G) is the minimum degree of G. Furthermore, we obtain an upper bound for k-restricted edge connectivity.
36184486
Image-Based Surface Detail Transfer
We present a novel technique, called Image-Based Surface Detail Transfer, to transfer geometric details from one surface to another with simple 2D image operations. The basic observation is that, without knowing its 3D geometry, geometric details (local deformations) can be extracted from a single image of an object in a way independent of its surface reflectance, and furthermore, these geometric details can be transferred to modify the appearance of other objects directly in images. We show examples including surface detail transfer between real objects, as well as between real and synthesized objects.
2276524
Automatic Business Card Scanning with a Camera
In this paper, we present a system to automatically extract, rectify and enhance business card images. First the business card image patch is automatically segmented by minimizing a novel local-global variational energy. Second a quadrangle is fitted to the segmented image patch. With the four corner points of the quadrangle, we then estimate the physical aspect ratio of the business card and obtain a homography to rectify the quadrangle back to rectangular shape. We finally enhance the contrast of the rectified business card image using a S-shaped curve. Extensive experiments demonstrated the efficacy and robustness of our system.
17488685
Large deviations and the generalized processor sharing scheduling for a two-queue system
We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks.
383050
A Domain Decomposition Method for Fast Manifold Learning
We propose a fast manifold learning algorithm based on the methodology of domain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problem that can glue the embeddings on the two subdomains into an embedding on the whole domain. We provide a detailed analysis to assess the errors produced by the gluing process using matrix perturbation theory. Numerical examples are given to illustrate the efficiency and effectiveness of the proposed methods.