Analysis Of Queueing Networks Research Articles

Design of fork-join networks of First-In-First-Out and infinite-server queues applied to clinical chemistry laboratories

This paper considers optimal design of queueing networks in which each node consists of a single-server FIFO queue and an infinite-server queue, which is referred to as incubation queue. Upon service completion at a FIFO queue, a job splits (forks) into two parts: the first part is routed to the next node on its route, and the second part is placed in the incubation queue. Routing of the jobs of multiple types is governed by a central decision maker that decides on the routes for each job type and aims to minimize the mean turnaround time of the jobs, i.e., the time spent in the system until service completion at the FIFO queue in the last node, and at all incubation queues on the job’s route, which may be viewed as a join operation. We provide explicit results for the turnaround time when all service and inter-arrival time distributions are exponential and invoke the Queueing Network Analyzer when these distributions are general. We then develop a Simulated Annealing approach to find the optimal routing configuration. We apply our approach to determine the optimal routing configuration in a chemistry analyzer line.

Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

A robust queueing network analyzer based on indices of dispersion

AbstractWe develop a robust queueing network analyzer algorithm to approximate the steady‐state performance of a single‐class open queueing network of single‐server queues with Markovian routing. The algorithm allows nonrenewal external arrival processes, general service‐time distributions and customer feedback. The algorithm is based on a decomposition approximation, where each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance‐time curve, called the index of dispersion for counts (IDC). The required IDC functions for the external arrival processes can be calculated from the model primitives or estimated from data. Approximations for the IDC functions of the internal flows are calculated by solving a set of linear equations. The theoretical basis is provided by heavy‐traffic limits for the flows established in our previous papers. A robust queueing technique is used to generate approximations of the mean steady‐state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm's effectiveness is supported by extensive simulation studies.

Modeling of an immune response: Queuing network analysis of the impact of zinc and cadmium on macrophage activation.

Chronic obstructive pulmonary disease is characterized by progressive, irreversible airflow obstruction resulting from an abnormal inflammatory response to noxious gases and particles. Alveolar macrophages rely on the transcription factors, nuclear factor κB and mitogen-activated protein kinase, among others, to facilitate the production of inflammatory mediators designed to help rid the lung of foreign pathogens and noxious stimuli. Building a kinetic model using queuing networks, provides a quantitative approach incorporating aninitial number of individual molecules along with rates of the reactions in any given pathway. Accordingly, this model has been shown useful to model cell behavior including signal transduction, transcription, and metabolic pathways. The aim of this study was to determine whether a queuing theory model that involves lipopolysaccharide-mediated macrophage activation in tandem with changes in intracellular Cd and zinc (Zn) content or a lack thereof, would be useful to predict their impact on immune activation. We then validate our model with biologic cytokine output from human macrophages relative to the timing of innate immune activation. We believe that our results further prove the validity of the queuing theory approach to model intracellular molecular signaling and postulate that it can be useful to predict additional cell signaling pathways and the corresponding biological outcomes.

A STUDY OF IMPROVING HOSPITAL OUT PATIENT DEPARTMENT (OPD) USING QUEUING NETWORK ANALYSIS METHODOLOGY

Service time and waiting time in hospitals are of growing importance in quality healthcare delivery. Long waiting times for health care is a critical issue in many countries. Many of the countries have now introduced benchmarks for that. The objective of this research paper is to study the Out Patient Department (OPD) of a hospital using queuing network analysis. The study aims to analyze the patient flow system by measuring the length of stay, service and waiting time distribution of patients and waiting time between two consecutive services availed/treatment undergone/department visited were calculated in an Out Patient Department (OPD) of a multispecialty hospital. There are major differences in how waiting times are measured: waiting period for kind of care/services the patient is waiting for; the parameters used; and where in the patient journey the measurement begins. We investigated the waiting time for patients before and during availing any of the services of multispecialty, rural based hospital in Gujarat, India. Various descriptive statistics analyses of routine data for 438 patients determined the association between selected patient characteristics, service time and waiting time. The median time spent by a patient (between patients enters in the hospital, being seen by a physician/availing various services and leaves the hospital is 44 minutes (within a range of 7.59–382 minutes). Day of arrival, time of arrival and service/ treatment category were significantly associated with waiting time. Variability in waiting times could be addressed by more standardized hospital operations, but may also be influenced by other clinical or non-clinical factors that require further investigation.

Big Data Analytics and Network Calculus Enabling Intelligent Management of Autonomous Vehicles in a Smart City

Artificial intelligence (AI) and big data analytics enable autonomous vehicles (AVs) to dramatically change future intelligent transportation in smart cities. AVs are envisaged to evolve to a service rather than a product in the future. To provide best user experience of such services, three primary factors, namely, waiting time, travel time, and supply of AV services, are taken into consideration in a multiobjective optimization. Conventional optimization of services relies on traffic flow analysis over a queuing network model. However, due to the mobility of vehicles and the transfer uncertainty of road networks, the queuing network analysis is too complicated and practically intractable. For accuracy and convenient processing, network calculus (NC) is extended to model the queueing problem in this paper. The optimal number of available AVs can be identified by guaranteeing the waiting time of customers. The satisfaction of AV services can be viewed as a supply and demand problem, and optimized by bipartite graph matching. In order to reduce the average travel time, especially for rush hours with heavy traffic, we further propose a new online AVs fleet management scheme with congestion control for smart cities. It is shown that the intelligent management of AV fleet can be efficiently achieved, outperforming the cases of traditional vehicles. NC-assisted AI enables an efficient intelligent transportation paradigm in smart cities, while achieving substantial energy saving.

Solving Problem of Optimal Placement Information Resources on the Nodes of a Distributed Information Processing System with a Self-Similar Input Flow of Applications

This article presents the results of numerical experiments to solve the problem of optimal placement of information resources on the nodes of a distributed information processing system (DIPS) by the criterion of the minimum average response time of the system to user requests, implemented on the basis of the architecture "file-server", two-level and three-level architecture "client-server" with self-similar input traffic applications. Approximate methods of stochastic Queuing networks research (decomposition approximation method and mean value analysis method) and simulation method were used as modeling methods. The obtained results of numerical experiments are compared with the results of solving the same problems using the exact method of analysis of exponential Queuing networks. By results of the comparative analysis of the received results conclusions are drawn.

Heavy-Traffic Limit of the GI/GI/1 Stationary Departure Process and Its Variance Function

Heavy-traffic limits are established for the stationary departure process from a GI/GI/1 queue and its variance function. The limit process is a function of the Brownian motion limits of the arrival and service processes plus the stationary reflected Brownian motion (RBM) limit of the queue-length process. An explicit expression is given for the variance function, which depends only on the first two moments of the interarrival times and service times plus the previously determined correlation function of canonical (drift −1, diffusion coefficient 1) RBM. The limit for the variance function here is used to show that the approximation for the index of dispersion for counts of the departure process used in our new robust queueing network analyzer is asymptotically correct in the heavy-traffic limit.

Performance analysis of open general queuing networks with blocking and feedback

Queuing network models have been extensively used for performance evaluation in many modern manufacturing and communication systems. The phenomenon of feedback reflects many practical situations, e.g. reworking in the production systems. However, existing research on open queuing network with feedback mainly concentrates on the models with infinite buffers or the models with finite buffers but exponentially distributed inter-arrival and service times. Research on open queuing networks with finite buffers, feedback and general inter-arrival and service times has not been reported. In this paper, a Rate Iterative Method embedded with the Generalised Expansion Method, is proposed for modelling this type of queuing network. System performance measures include the mean throughput, work-in-process and sojourn time all calculated by the proposed method. The accuracy and the efficiency of the proposed method are tested by comparing the results with other methods or simulation results from the experiments. Finally, a case study of a practical production system used in the manufacturing industry is studied and illustrates the applications of the proposed method. The results in this paper can be used as a basis for system design analysis and resource planning.

Queuing Network Modeling and Analysis of Manufacturing System with AGV with Multi-section-annular Path

Queuing Network Modeling and Analysis of Manufacturing System with AGV with Multi-section-annular Path

Adaptive Control Channel Interval in VANET Based on Mobility Model and Queuing Network Analysis

The dynamic of changing network topology and vehicle density in VANET are causing the dynamic of message traffic intensity. This situation requires adaptability of channel management to provide the channel capacity dynamically and proportionally. The length of CCH interval in VANET represents the capacity of channel or service rate of vehicles. The fixed pattern of CCH/SCH interval as published by IEEE 802.11p/1609.4 would become the constraint of adaptability of vehicles in VANETs. Moreover it would affect to VANET performance inefficient. This research proposes an adaptive scheme of CCH/SCH interval which proportional with density of vehicles based on the number of vehicle connected each other’s. To show how effective the proposed adaptive scheme of CCH/SCH interval can afford to improve of VANET performance (compared to fixed interval scheme of current IEEE standard), we analyze by combining mobility model and queuing network model. We assume that statistically there is a steady state of VANET topology which can be analyzed by using queuing network model. We specified the real map of highway in Bandung city along 10 Km length to achieve the representative experimental result. The various specified of speeds are: 70-90 Km/h, 90-110 Km/h, and 110-130Km/h, while the various of density of vehicle are 15, 30, 45, 60, 75, and 90 vehicles along 10Km length of highway. All of experiments performed in two main scenarios, i.e. the fixed CCH/SCH interval, and adaptive CCH/SCH interval which compared each other to see the improvement. The analytical result examined by simulation method. The experimental results show the improvement of adaptive CCH/SCH interval. The improvement of average delay is 10ms, and the improvement of system throughput is 450 kbps.

FINDING SHORTEST ROUTING SOLUTION IN MOBILE AD HOC NETWORKS USING FIREFLY ALGORITHM AND QUEUING NETWORK ANALYSIS

Mobile ad hoc network (MANET) is a group of mobile nodes establishing a wireless network without using centralized and fixed infrastructure. In MANET, nodes may function as hosts and routers. The nodes can move freely and in arbitrary ways. The network topology in MANET is dynamic because of the frequent mobility of nodes, thus routing is challenging aspects in MANET. Routing protocol plays a role in choosing and selecting the optimal route for transferring the packets of data from the source node to the destination node efficiently. Mostly the previous routing protocols are not practical to this dynamic network topology. Therefore designing an efficient routing protocol for this dynamic network is vital issue. In this paper, the author has proposed an approach, which selects shortest route for transferring the packets of data from source node to the destination node combining firefly algorithm and queuing network analysis. Firefly algorithm can be applied to find the shortest route in this routing problem. The response times taken to send packets of data can be calculated using the suggested queuing model. The result reveals that attractiveness of node in MANET decreases with the increasing value of response time.

Performance Analysis of CPU-GPU Cluster Architectures

High performance computing (HPC) encompasses advanced computation over parallel processing, enabling faster execution of highly compute intensive tasks such as climate research, molecular modeling, physical simulations, cryptanalysis, geophysical modeling, automotive and aerospace design, financial modeling, data mining and more. High performance simulations require the most efficient compute platforms. The execution time of a given simulation depends upon many factors, such as the number of CPU/GPU cores and their utilization factor and the interconnect performance, efficiency, and scalability. CPU and GPU clusters are one of the most progressive branches in a field of parallel computing and data processing nowadays. GPUs have become increasingly common in supercomputing, serving as accelerators or "co-processors" in every node CPU-GPU to help CPUs get work done faster. In this paper I use the Multiclass Closed Product-Form Queueing Network (MCPFQN) and Mean Value Analysis (MVA) to analyze effects of the CPU-GPU cluster interconnect on the performance of computer systems.

Finite Queueing Modeling and Optimization: A Selected Review

This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method. Secondly, different model approaches are described and optimized with regard to the key parameters in the network (e.g., buffer and server sizes, service rates, and so on).

Performance analysis of wireless sensor networks using queuing networks

Wireless Sensor Networks (WSNs) are autonomous wireless systems consists of a variety of collaborative sensor nodes forming a self-configuring network with or without any pre-defined infrastructure. The common challenges of a WSN are network connectivity, node mobility, energy consumption, data computation and aggregation at sensor nodes. In this paper we focus on intermittency in network connectivity due to mobility of sensor nodes. We propose a new mathematical model to capture a given entire WSN as is with intermittency introduced between the communication links due to mobility. The model involves open GI/G/1/N queuing networks whereby intermittency durations in communication links are captured in terms of mobility models. The analytical formulas for the performance measures such as average end-to-end delay, packet loss probability, throughput, and average number of hops are derived using the queuing network analyzer and expansion method for models with infinite- and finite-buffer nodes, respectively. For models with 2-state intermittency, we analyze the performance measures by classifying these models into three types: namely, model with intermittent reception, model with intermittent transmission and/or reception, and model with intermittent transmission. We extend the analysis to multi-state intermittency models. We demonstrate the gained insight of WSNs through extensive numerical results.

Batch sizes optimisation by means of queueing network decomposition and genetic algorithm

Batch sizes have a considerable impact on the performance of a manufacturing process. Determining optimal values for batch sizes helps to reduce inventories/costs and lead times. The deterministic nature of the available batch size optimisation models reduces the practical value of the obtained solutions. Other models focus only on critical parts of the system (e.g., the bottleneck). In this paper, we present an approach that overcomes important limitations of such simplified solutions. We describe a combination of queueing network analysis and a genetic algorithm that allows us to take into account the real characteristics of the system when benefiting from an efficient optimisation mechanism. We are able to demonstrate that the application of our approach on a real-sized problem with 49 products allows us to obtain a solution (values for batch sizes) with less than 4% relative deviation of the cycle time from the exact minimal value.

Impact of source counter on routing performance in resource constrained DTNs

We study routing schemes for Disruption Tolerant Networks (DTNs) where transmission bandwidth is scarce. In such a setting, a key issue is how to schedule the transmission of packets under limited bandwidth to optimize performance. Such a scheduling consists of source control (i.e., source nodes choosing a routing scheme) and the local transmission scheduling performed by each node. Existing works typically focus on transmission scheduling and buffer management aspects, but due to theoretical and practical difficulties, only heuristics have been proposed. In this work, we explore an alternative way to improve DTN routing performance via source control. We first show through simulation that for spray-and-wait routing scheme where the source node specifies the maximum allowed number of copies of a packet in the network, there exists an optimal counter value that achieves the minimum network-wide average packet delivery delay. Then as a first step towards understanding multi-hop multi-copy DTN routing schemes such as spray-and-wait scheme, we perform modeling study of two-hop single-copy scheme and two-hop multi-copy scheme under various transmission scheduling schemes, via queuing network analysis and continuous time Markov chain model analysis. Our modeling analysis provides insights into the impact of source counter on routing performance and further suggests the existence of an optimal counter value. Relying on the insights gained via simulations and modeling studies, we propose an adaptive scheme where nodes adjust their counter values to achieve minimum packet delivery delay, in a distributed and asynchronous fashion. Simulations demonstrate the effectiveness of our scheme and suggest the potential of exploring this rich area for improving DTN routing performance.

Modelling traffic congestion using queuing networks

Traffic studies have been carried out predominantly using simulation models which are both time and capital intensive. In this paper, an analytical model of uninterrupted single-lane traffic is proposed using queuing analysis. Well-known Traffic Flow-Density diagrams are obtained using simple Jackson queuing network analysis. Such simple analytical models can be used to capture the effect of non-homogenous traffic.

A joint moments based analysis of networks of MAP/MAP/1 queues

The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues with FIFO scheduling is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilizing recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.

A traffic based decomposition of two-class queueing networks with priority service

This paper presents a Markov arrival process (MAP) based methodology for the analysis of two-class queueing networks with priority service nodes. We apply the multi-class extension of MAP, referred to as Marked MAP (MMAP), for the description of the input and internal traffic in the queueing network. The MMAP traffic description allows to capture not only the dependency structure of the traffic classes themselves, but also the inter-class dependency of the high and low priority traffic. To carry out MMAP based queueing network analysis the paper presents several contributions: the departure process analysis of the MMAP/MAP/1 priority queue, an MMAP construction method based on the joint moments of two consecutive inter-departure times and some new results towards the efficient performance analysis of the MMAP/MAP/1 priority queue. Numerical examples illustrate the accuracy of the proposed traffic based decomposition method.