36195188
On the Three Threshold Policy in the Multi-Server Queueing System with Vacations
In this paper, we study an M/M/c queue with a three threshold vacation policy denoted by (e, d, N). With such a policy, the servers keep serving the customers until the number of idle servers reaches d and then e of d servers start taking a vacation together. These e servers keep taking vacations until the number of customers in the system is at least N at a vacation completion instant, then the e servers return to serve the queue again. Using the matrix analytic method, we obtain the stationary performance measures and prove the conditional stochastic decomposition properties for the waiting time and queue length. This model is a generalization of previous multi-server vacation models and offers a useful performance evaluation and system design tool in multi-task server queueing systems.
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.
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.
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.
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.
5688571
Enhancing Downlink Performance in Wireless Networks by Simultaneous Multiple Packet Transmission
In this paper, we consider using simultaneous Multiple Packet Transmission (MPT) to improve the downlink performance of wireless networks. With MPT, the sender can send two compatible packets simultaneously to two distinct receivers and can double the throughput in the ideal case. We formalize the problem of finding a schedule to send out buffered packets in minimum time as finding a maximum matching problem in a graph. Since maximum matching algorithms are relatively complex and may not meet the timing requirements of real-time applications, we give a fast approximation algorithm that is capable of finding a matching at least 3/4 of the size of a maximum matching in O(|E|) time, where |E| is the number of edges in the graph. We also give analytical bounds for maximum allowable arrival rate, which measures the speedup of the downlink after enhanced with MPT, and our results show that the maximum arrival rate increases significantly even with a very small compatibility probability. We also use an approximate analytical model and simulations to study the average packet delay, and our results show that packet delay can be greatly reduced even with a very small compatibility probability.
3877390
Distributed meetings: a meeting capture and broadcasting system
The common meeting is an integral part of everyday life for most workgroups. However, due to travel, time, or other constraints, people are often not able to attend all the meetings they need to. Teleconferencing and recording of meetings can address this problem. In this paper we describe a system that provides these features, as well as a user study evaluation of the system. The system uses a variety of capture devices (a novel 360° camera, a whiteboard camera, an overview camera, and a microphone array) to provide a rich experience for people who want to participate in a meeting from a distance. The system is also combined with speaker clustering, spatial indexing, and time compression to provide a rich experience for people who miss a meeting and want to watch it afterward.
18001096
Optimal scheduling algorithms in WDM optical interconnects with limited range wavelength conversion capability
Optical communication is a promising candidate for many emerging networking and parallel/distributed computing applications because of its huge bandwidth. Wavelength division multiplexing (WDM) is a technique that can better utilize the optical bandwidth by dividing the bandwidth of a fiber into multiple wavelength channels. In this paper, we study optimal scheduling algorithms to resolve output contentions in bufferless time slotted WDM optical interconnects with wavelength conversion ability. We consider the general case of limited range wavelength conversion with arbitrary conversion capability, as limited range wavelength conversion is easier to implement and more cost effective than full range wavelength conversion, and it also includes full range wavelength conversion as a special case. We first consider the conversion scheme in which each wavelength can be converted to multiple wavelengths in an interval of wavelengths and the intervals for different wavelengths are "ordered". We show that the problem of maximizing network throughput can be formalized as finding a maximum matching in a bipartite graph. We then give an optimal scheduling algorithm called the first available algorithm that runs in O(k) time, where k is the number of wavelengths per fiber. We also study the case where the connection requests have different priorities. We formalize the problem as finding an optimal matching in a weighted bipartite graph and give a scheduling algorithm called the downwards expanding algorithm that runs in O(kD + Nklog(Nk)) time where N is the number of input fibers of the interconnect and D is the conversion degree. Finally, we consider the circular symmetrical wavelength conversion scheme and give optimal scheduling algorithms for nonprioritized scheduling in O(Dk) time and prioritized scheduling in O(k/sup 2/+Nklog(Nk)) time.
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.
28168487
Channel condition ARQ rate control for real-time wireless video under buffer constraints
Many emerging applications involve real-time packet video transmission over noisy wireless networks. To ensure reliable video transmission, an automatic repeat request (ARQ) scheme is used for repairing packet loss over a channel by retransmitting corrupted packets. However, an ARQ resolves the problem of packet loss at the expense of varying an effective channel rate as well as introducing extra latency. These properties increase the difficulty of rate control for real-time wireless video when the buffer overflow and underflow are taken into account. Therefore, we propose a novel ARQ-based rate control scheme, called "channel condition ARQ rate control" by using embedded coding to design an efficient retransmission policy for wireless video. This scheme achieves both maximal channel utilization and smooth video quality perceived at an end-host, which has a low implementation complexity under buffer constraints. We have conducted extensive simulations to verify the efficiency and robustness of the proposed scheme.