Control charts for traffic intensity monitoring of Markovian multiserver queues

A number of recent research studies have applied queueing theory as an approximate modeling tool to mathematically describe industrial systems, which include manufacturing, distribution, and service, for instance. Among the main observable characteristics in queues, the number of users in the system can be controlled to keep waiting times as minimal as possible. The design of efficient control charts is an attempt to monitor and control such systems. Control charts are proposed to monitor infinite queues with Markovian arrivals, exponential service times, and s identical parallel servers. The proposed charts monitor traffic intensities, which are the ratio between the arrival rate and the service rate, estimated through the number of users in the queueing system at random epochs. The effectiveness and efficiency of the proposed approaches in terms of the average run lengths are established by a comprehensive set of Monte Carlo simulations.     

Modelling of material handling systems for facility design in manufacturing environments with job-specific routing

Traditionally, flow times distance is used as a surrogate for cost in facility design. However, this performance measure does not fully capture the impact of facility design decisions on operational performance measures such as cycle time and work-in-progress in the system, which are often more meaningful for managers, especially in a manufacturing environment. To better measure operational performance, modelling of material handling systems using a queueing network must be integrated in the facility design process. A number of approaches are discussed in the facility design literature for modelling material flow using queueing networks. In these approaches, Poisson arrival or Markovian job routing assumptions have been used. However, for many manufacturing environments, these assumptions lead to an inaccurate estimation of the material handling system's performance and thus lead to poor facility designs. Incorporating more general queueing results for non-Markovian systems is difficult, however, because the facility design process must investigate a large number of potential solutions and thus the results from the queueing models for the material handling system must be quickly obtained. In this paper, the need for more general queueing models of material handling systems in facility design is confirmed. Then, an approach based on multi-class queueing models is adapted to capture the change in variability of the system performance caused by both different arrangements of workstations in the facility and different arrival processes to the workstations due to the job routing in a computationally efficient manner. The proposed modelling approach is shown to provide more accurate results than previous methods used in facility design based on numerical comparisons with results from discrete-event simulation.     

Stability and robustness of time‐delay systems

Abstract

Using some properties of matrix measures and matrix's spectral radius, a new stability criterion for a linear time‐delay system is derived. This result is also extended to interval time‐delay systems.     

Multi‐rate digital control for a cascaded system consisting of two subsystems with different input time delays

Abstract

This paper presents a multi‐rate state‐space control scheme for digital control of a cascaded continuous‐time system with fractional time delays. First, a discrete‐time state‐space representation of a continuous‐time system with a fractional input delay is established. Based on the time‐delay digital modelling, an ideal state reconstructor is also presented such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. Next, a time‐delay subsystem (designated subsystem 1) with a fast sampling rate is designed to form the inner loop of the overall system, then the designed closed‐loop subsystem 1 is cascaded with a time‐delay open‐loop subsystem 2 with a slow sampling rate. A digital modelling of the time‐delay open‐loop subsystem 2, based on a fast‐rate sampling, is also formed for obtaining the digital modelling of the overall cascaded continuous‐time system by using the block‐pulse function approximation. Then, the fast‐rate overall system is converted into a slow‐rate model via the newly developed model conversion technique. Furthermore, subsystem 2 is separated from the slow‐rate overall system via a linear transformation for achieving a reduced‐order subsystem design. As a consequence, a digital control law is determined on some specific goals for the overall system. The proposed method is suitable for digital control of a multivariable, multi‐rate, time‐delay system in which state variables are not accessible.     

Performance evaluation of a finite queue with random routing

Abstract

In previous papers [1–3], the steady‐state behavior of a finite queue which accepts batch Poisson inputs and receives service operating in the synchronous mode was studied. Analysis was successfully completed via the application of the Residue theorem in complex variables. This paper extends the work to include the effect of routing. Two types of random routing are considered in this paper. Results obtained include state‐transition probability, blocking probability, delay, and throughput. Validity of analysis has been verified by computer simulation.     

Graph contractability problem for VLSI layer assignment

Abstract

The layer assignment problem for VLSI routing is the problem of determining which layers can be used for routing the wire segments in the interconnections of nets so that the number of vias is minimized. In this paper, we transform the problem of layer assignment for three‐layer routing to the contractability problem of 3‐colorable graph. This problem is shown to be NP‐complete and a heuristic algorithm is proposed on the basis of the graph contractability model. From our experimental results, the algorithm is faster and efficient to generate very good results. In the average, the number of vias can be reduced by 30 percent or so.     

Performance analysis of an inbound call center with skills-based routing

Many call centers provide service for customers of different classes with differently qualified groups of agents. Since call arrivals and call handling times are random in inbound call centers, we investigate queueing models for their performance analysis. This paper describes a Markov queueing model with two customer classes and three groups of specialized or flexible agents. The mean call handling time may depend on the respective customer class as well as on the agent group serving this call. The customers are assumed to be impatient. We consider skills-based routing with priority-based rules and derive both steady-state probabilities and performance measures. We present some numerical experiments and show the impact of different mean processing times. The influence of the allocation of the agents into the three groups is analyzed for different levels of patience.Correspondence to: Raik Stolletz . R. Stolletz, S. Helber: The authors thank the anonymous referees for their helpful comments and suggestions.     

A discrete‐time multiqueue‐multiserver system with time‐division multiplexed services and non‐zero walktime

Abstract

This paper presents results for an N‐queue system which receives services from M equal‐speed servers under time division multiplexed manner. When served, each customer consumes fixed service time and departs. One practical constraint imposed is the non‐zero walktime consumed by a server when it undertakes the transition of its service from one queue to another. Two types of inputs, synchronous and asynchronous, are considered in this paper.     

Square and Rectangular Symmetry Tiles from Bulk and Thin Film 3‐Miktoarm Star Terpolymers

The directed self assembly of a 3‐miktoarm star terpolymer (polyisoprene‐arm‐polystyrene‐arm‐polyferrocenylethylmethylsilane (3μ‐ISF)) into a (4.8²) square symmetry Archimedean tiling pattern is described. Bulk samples of 3μ‐ISF generate equilibrium columnar (4.8²) tile patterns (symmetry p 4 mm) on annealing, which is preceded by a metastable c 2 mm centered rectangular structure. In contrast, in thin films of 3μ‐ISF blended with PS homopolymer, the c 2 mm phase is stable with columns oriented out of plane when the film thickness is below 50 nm. However, the 3μ‐ISF/homopolymer blend rapidly forms a p 4 mm symmetry when the film thickness is ～80 nm, with grain sizes of several μm and excellent order. Defects in the p4mm structure are described.     

Optimal memoryless strategies of a two‐rate communication link

Abstract

Game theory has been applied to study the performance of a communication system in a hostile environment. By appropriately choosing the payoff, a communication system in the presence of a hostile jammer can be modeled as a finite two‐person zero‐sum game. In this paper, we model a two‐rate communication link interfered by an on‐off jammer as a two‐person zero‐sum game and derive the optimal memoryless communication and jamming strategies. The ensemble mean of the time average throughput is considered as the payoff to the communicator. It is found that, under average jamming power constraints, the optimal memoryless jamming strategy is, in general, to allocate as much jamming power as possible to one direction. We study both symmetric and asymmetric communication strategy cases. The performance of the communication system is better if an asymmetric communication strategy is adopted. However, the system resulting from an optimal asymmetric communication strategy may become non‐ergodic.     

Iterative optimization for joint design of source and channel codes using genetic algorithms

Abstract

This paper presents a novel algorithm for the joint design of source and channel codes. In the algorithm, channel‐optimized vector quantization (COVQ) and rate‐punctured convolutional coding (RCPC) are used for design of the source code and the channel code, respectively. We employ the genetic algorithm (GA) to prevent the design of COVQ from falling into a poor local optimum. We also adopt the GA to reduce the computational time needed for realizing the unequal error protection scheme best matched to the COVQ. Both the GA‐based source coding and channel coding scheme are then iteratively combined to achieve a near global optimal solution for the joint design. Numerical results show that the algorithm can be an effective alternative for applications where high rate‐distortion performance and low computational complexity are desired.     

间断连通移动有组织网络中延时有界的概率路由策略

针对间断连通移动自组织网络(ICMAN)实际应用中对消息的送达率、发送延时及开销三项重要指标的要求,本文借助于发送延时的概率模型,分析了这三项指标的相互关系,进而提出了一种综合考虑这三种指标的延时有界的概率路由策略(BDPBR),其特点是重视精确的延时指标,而非现有算法关注的消息的平均传输延时,能以给定概率保证消息的端到端发送延时.仿真结果表明,该策略能够通过调整必需发送概率(RDP)和必需传输延时(RDD)来控制消息的实际发送率和发送延时,同时可根据RDP和RDD来调整系统开销,可按用户设定的送达率与延时指标以相应的代价发送消息,适应不同的服务要求.     

Interaction between radio link level truncated ARQ, and TCP in multi-rate wireless networks: a cross-layer performance analysis

A complete queueing model for radio link layer performance analysis is developed assuming adaptive modulation and coding (AMC) at the physical layer and truncated automatic repeat request (ARQ)-based error control at the link layer. From the model, queue length distribution and average queueing delay can be calculated. The average queueing delay is then used to estimate transmission control protocol (TCP) throughput performance using a fixed-point approach. Using the model, we are able to choose signal-to-noise ratio thresholds of different transmission modes for AMC at the physical layer for different persistence levels of ARQ at the link layer so that TCP throughput is maximized. We observe that channel correlation negatively impacts the TCP throughput performance. Also, throughput enhancement of TCP NewReno over TCP Reno is observed to be non-negligible only if no ARQ-based error recovery is employed at the link layer.     

On a Multichannel Queueing System with Ordered Entry and Heterogeneous Servers

A multichannel queueing system with ordered entry and no waiting line is considered under the assumption of Poisson arrival and negative exponential service with a different rate in each channel. For the system with two or three heterogeneous servers, the best servers' arrangement is established by interchanging the order of servers to decrease the overflow probability and thereby increase the number of items serviced per unit time. The system considered is a simplified model for a production system with a closed loop conveyor.     

Array sensor spacing for optimal time‐delay estimation

Abstract

The effects of sensor spacing on the performance of time‐delay estimation are considered. For narrow‐band signals the array aperture and sensor spacing seriously change the estimation result. The post beamforming signal‐to‐noise ratio is also important for choosing the sensor spacing. The conventional half wavelength spacing is shown to be the only one of the many choices towards achieving a similar estimation performance.     

Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.     

Erlang消失系统空闲服务台的利用

本文研究Erlang消失系统中空闲服务台的利用,该系统中有两类顾客,一类有抢占型优先权,并且是消失的;另一类可排队等待,并有无限等待空间。使用拟生灭过程和矩阵几何解,给出系统稳定的充分必要条件,第一类顾客消失概率、第二类顾客的队长和等待时间分布。数值例子解释了系统性能指标与参数之间的关系。     

Analysis of a single stage production system with heterogeneous machines

The performance of a single stage production system with two heterogeneous machines and two classes of jobs is investigated. The machines have a common buffer with jobs of both classes waiting for service. The arrivals are assumed to follow a Poisson process and the service times to be distributed exponentially. The evaluated production system differs from a classical homogeneous multiple server queueing system with regard to inhomogeneities of the two machines. Time inhomogeneity – the service times of the two machines being unequal – and functional inhomogeneity – one of the machines can handle only one class (A) of jobs – are to be distinguished. In the case of time inhomogeneity the calculation of system performance parameters may be carried out using an explicit formula, whereas for the analysis of functional inhomogeneity a numerical solution has to be derived. The impact of time inhomogeneity is very small and decreases with the system workload. On the contrary, functional inhomogeneity leads to elevated cycle times of up to 40% depending on the degree of inhomogeneity (measured by the fraction of A jobs) and the workload. Therefore, in contrast to the time-inhomogeneous case, single stage production systems with functional inhomogeneity can only be approximated tolerably by a homogeneous multiple server queueing system if the fraction of one-machine jobs is less than 30%. The increased throughput times above 30% are supplied by the diagram developed from the numerical solutions. RID="*" ID="*" While this research was constructed the author was affiliated to Institute of Conveying Technology and Logistics. Correspondence to: C. R. Lippolt     

A pinwheel packet scheduling scheme for broadband wireless networks

Abstract

A frame‐based packet scheduling scheme, the pinwheel scheduling (PWS) scheme, is proposed and investigated at the medium access control (MAC) layer in broadband wireless networks. The objective of the proposed scheduling scheme is to provide low delay and low jitter for real‐time traffic. We have demonstrated in this paper that the proposed PWS scheme not only satisfies the packet‐level QoS requirements but also has low implementation cost. The PWS scheme gives the highest priority to CBR connections in a service cycle to minimize their delay and jitter. For ABR traffic, a number of slots are allocated to fit their MCR. The remaining time slots are then allocated to VBR traffic according to their PCR. Thus, the VBR traffic may suffer large delay and jitter when the number of CBR connections increases. The PWS with modular strategy (PWS/MS) is proposed to improve the performance of the VBR traffic. We also introduce three different slot‐reuse strategies named real‐time traffic first (RTF), non‐real‐time traffic first (NRTF) and longest queue first (LQF), respectively, to improve resource utilization. In order to demonstrate the performance of the PWS and PWS/MS schemes, comparisons are made with existing schemes such as the round‐robin (RR) and weighted‐round‐robin (WRR) by using OPNET software. Simulation results show that the proposed schemes are capable of maintaining the lowest delay and jitter for VBR and CBR traffic while not sacrificing the available bit rate (ABR) traffic.     

Markovian Queues with Three Heterogeneous Servers1

In this article a Markovian queueing system with three heterogeneous servers is considered. The system is such that the first server works faster than the second, and the second works faster than the third. This heterogeneous system is compared to the corresponding homogeneous system, and conditions showing its efficiency are obtained. The problem of obtaining the best service rates, which minimize the average characteristics of the heterogeneous system, is investigated numerically. Tables representing the sequences of the best service rates, and the average characteristics of both the heterogeneous and the homogeneous systems are given.