Finite Queueing Model Research Articles

Performance analysis and cost investigations for state-dependent single unreliable server finite queue under F-policy using GA and QNM

State-dependent queues are essential as they accurately capture the dynamic behavior of systems, enabling more realistic modeling and analysis of various real-world scenarios. The present investigation deals with a state-dependent single unreliable server finite queueing model under admission control F-policy. The admission control F-policy is a valuable tool to control the congestion problem of customers where the queue forms. In the proposed model, the server is prone to breakdown and can fail at any time. There is a two-phase repair facility available to address server failures. Chapman–Kolmogorov (C–K) steady-state equations based on the birth–death process are formed and solved using the matrix analytic method to formulate a mathematical model. By setting suitable values for state-dependent parameters, some particular models, such as the machine repair problem (MRP) and queueing model with customers’ balking and feedback, can also be deduced. Furthermore, various queueing indices are established to predict the validity of state-dependent queues. A total cost function for the system is constructed to enhance customer service while minimizing costs. This cost function is then optimized using a genetic algorithm (GA) and quasi-Newton method (QNM). The cost optimization in the state-dependent queueing model enables businesses to optimize resource allocation and achieve cost-efficient service delivery, leading to improved profitability and customer satisfaction.

On the rate of convergence for a class of Markovian queues with group services

There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function is not applicable here. This approach gives sharp bounds for the situation of essentially non-negative matrix of the corresponding system, but in our case it does not hold. Here we use the method of differential inequalities to obtaining bounds on the rate of convergence to the limiting characteristics for the class of finite Markovian queueing models. We obtain bounds on the rate of convergence and compute the limiting characteristics for a specific non-stationary model too. Note the results can be successfully applied for modeling complex biological systems with possible single births and deaths of a group of particles.

Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

This paper deals with a finite capacity multi-server Markovian queueing model with Bernoulli feedback, synchronous multiple vacation policy and customers’ impatience (balking and reneging). By employing certain customer retention mechanism, impatient customers can be retained in the system. Applications of the suggested queueing model can be found in a wide variety of practical systems including modern information and communication technology (ICT) networks, call centers, and manufacturing systems. Using the recursive method, the steady state probabilities of the model are obtained. Various performance measures are derived. Then, some important particular cases are provided. Finally, different numerical examples are presented to demonstrate how the different parameters of the model influence the behavior of the stationary characteristics of the system.

Analysis of spectrum handoff delay using finite queuing model in cognitive radio networks

Analysis of spectrum handoff delay using finite queuing model in cognitive radio networks

Optimal Control F-policy for M/M/R/K Queue with an Additional Server and Balking

The multi-server finite queueing model with balking under admission control of customers based upon F-policy is investigated. In order to reduce the balking behavior of the customers, there is the provision of one additional server so as to shorten the queue length formed by the customers in rush hour. The noble realistic feature of the proposed Markov model is to control the admission of customers based on the threshold level ‘F’ of the queue size. According to ‘F’ policy, no more customers can be accommodated once the system is full and then after the further admission of the customers is not acceptable until the queue size drops to the predefined threshold level ‘F’. Chapman–Kolmogorov equations have been framed and are solved by using the recursive technique to establish the steady-state queue size probability distribution of the customers present in the system. A numerical example is taken to explore the various system indices. Adaptive neuro-fuzzy inference system (ANFIS) approach is applied to compare the soft computing results obtained by ANFIS with the results computed by the analytical method. The cost function is framed to determine the optimal control parameters namely threshold value ‘F’, the capacity of the system, the number of servers and service rate.

Analysis of Spectrum Handoff delay using Finite Queuing model in Cognitive Radio Networks

Spectrum handoff is an inevitable phenomenon to exploit dynamic spectrum access in cognitive radio networks (CRNs) for better spectrum utilisation. When a licensed or primary user reclaims its operating channel, the cognitive user has to initiate a suitable handoff procedure for successful completion of its ongoing transmission. This paper analyses the prioritised proactive spectrum handoff decision for a finite capacity cognitive radio network using preemptive resume priority (PRP) M/G/1/K queuing model. Cumulative handoff delay (CHD) and total service time (TST) are taken to investigate the performance of the handoff strategies. We establish an analytical model of cumulative handoff delay and total service time of proactive switching spectrum handoff for the proposed finite length queuing network. The impact of queue length on performance measuring metrics such as CHD and TST in terms of arrival rate of primary users and mobility factor of spectrum holes are presented extensively.

Analysis of the EDoS attack impact on elastic cloud services using finite queuing model

This paper proposes a logical model to examine the effect of the EDoS attack in cloud environment using finite queuing model and enhanced with experimental model. Due to this sophisticated attacks the computing resources are busy and buffer capacity of the cloud gets exhausted by both the legitimate and malicious user requests, because of this both types of requests could not get the service. The legitimate customers are unable to get service of web application. In this backdrop this paper investigates and evaluates the vendor loss factor from the cost factor of view since the legitimate client requests are denied service. The objective of this analysis is twofold i) to identify the dynamics of the EDoS attacks with different attack rates and to measure the various performance metrics (total number of busy virtual machines, utilization of the cloud resources, request response time, request loss probability, and throughput). ii) The cost function is defined and evaluated based on these performance metrics. Finally compared analytical and experimental results are presented and conclusions are drawn.

Performance modeling and analysis of hypoexponential network servers

Hypoexponential servers are commonly seen in today’s computer and communication networks whereby incoming packets are processed by the network server in multiple stages with each stage having a different processing time. This paper presents an analytical model to capture the behavior and subsequently analyze the performance of these network servers or similarly behaving systems. From our model, we derive key performance measures and features which include CPU utilization, system idleness, mean throughput, packet loss, mean system and queuing packet delays, and mean system and queue sizes. In addition, we present two popular finite queueing models (namely, M / D / 1 / K and M / M / 1 / K) to approximate our hypoexponential model. Results show that the both of these approximate models give close results when the system queue size is large.

Transient Analysis of Markovian Queue Model with Multi Stage Service

The present investigation deals with the transient analysis of Markovian queue model with multi stage service. Here, current analysis deals with M/M/1 queueing model with finite capacity. The arrival of the customer in the system follows Poisson process and the customers are served following exponential distribution. The brokendown server is immediately send for repair process so as to become as good as earlier. Transient analysis of finite Markovian queueing model has been studied using Runge-Kutta method. Various performance measures like queue length of the system, waiting time, throughput, service state probabilities have also been obtained.

Measurement of Mobile Switching Centres Throughput in GSM Network Integrating Sliding Window Algorithm with a Single Server Finite Queuing Model

The sliding window algorithm proposed for determining an optimal sliding window does not consider the waiting times of call setup requests of a mobile station in queue at a Mobile Switching Centre (MSC) in the Global System for Mobile (GSM) Communication Network. This study proposes a model integrating the sliding window algorithm with a single server finite queuing model, referred to as integrated model for measurement of realistic throughput of a MSC considering the waiting times of call setup requests. It assumes that a MSC can process one call setup request at a time. It is useful in determining an optimal sliding window size that maximizes the realistic throughput of a MSC. Though the model assumes that a MSC can process one call setup request at a time, its scope can be extended for measuring the realistic throughput of a MSC that can process multiple call setup requests at a time.

Analysis of single server finite queueing model with reneging

The present investigation deals with the analysis of Markovian queueing model with finite capacity and finite population wherein the server works in fast and slow random environments, depending on the status of service system, with exponential distributed time parameters. On arrival of the customer in slow mode, the exponential distributed time may be fixed. Due to the impatient behaviour (reneging), the customer may leave the queue after some time of joining the system if the server does not change its state before expiry of the timer. To discuss the behaviour of the queue length distribution and to obtain the transient solution, Runge-Kutta method of the fourth order is used. Various performance measures are determined in terms of transient probabilities of the system states. The numerical illustrations are facilitated to validate the tractability of performance measures as far as computational aspect is concerned.

A Cross-Layer Resource Allocation Algorithm with Dynamic Buffer Allocation Mechanism

A novel cross-layer wireless resource allocation algorithm called DBMQT is proposed which distributes the resource based on dynamic buffer allocation mechanism for orthogonal frequency division multiplex access (OFDMA) system. The aim of allocation algorithm is to maximize system throughput while satisfying the QoS requirement for multi-user and multi-service. The algorithm consists of two steps. Firstly, with the assumption of a finite queue model for arrival packets, the scheme adjusts users’ buffer according to dynamic buffer allocation mechanism. In the second step, a distinct scheduling priority is defined for each user integrates MAC QoS requirements, queue status and PHY Channel State Information (CSI), assuming that the power is uniformly allocated on each subcarrier. Using these scheduling priorities, a scheduling rule for mixed traffics is proposed. Simulation results indicate that the proposed algorithm can achieve better performance in terms of system throughput, packet loss rate and efficiency of the buffer than tradition algorithm under enhancing QoS guarantees for different services.

Packet-Based Modeling of Reed–Solomon Block-Coded Correlated Fading Channels Via a Markov Finite Queue Model

We consider the transmission of a Reed-Solomon (RS) code over a binary modulated time-correlated flat Rician fading channel with hard-decision demodulation. We define a binary packet (symbol) error sequence that indicates whether an RS symbol is successfully transmitted across the discrete (fading) channel whose input enters the modulator and whose output exits the demodulator. We then approximate the packet error sequence of the discrete channel (DC) using the recently developed queue-based channel (QBC), which is a simple finite-state Markov channel model with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> th-order Markovian additive noise. In other words, we use the QBC to model the binary DC at the packet level. We propose a general framework for determining the probability of codeword error (PCE) for QBC models. We evaluate the modeling accuracy by comparing the simulated PCE for the DC with the numerically evaluated PCE for the QBC. Modeling results identify accurate low-order QBC models for a wide range of fading conditions and reveal that modeling the DC at the packet level is an efficient tool for nonbinary coding performance evaluation over binary channels with memory.

Robustness of state-dependent queues and material handling systems

In many factory settings, performance modeling and optimisation of material handling systems (MHS) is a complex problem. State-dependent queueing models are effective and robust tools to capture this traffic congestion. The integration of state-dependent models of the material handling elements and finite queueing models of work stations is demonstrated. An important property of the state-dependent models when used to model the material handling elements is that they appear to be insensitive to the input distribution. Numerous topological network design (TND) problems and experiments are presented to show the effectiveness of state-dependent queueing models for TND/MHS design.

Transient Analysis of a Telecommunication System Using State Dependent Markovian Queue under Bi-Level Control Policy

Abstact. In this paper, we develop a finite queueing model having single and batch service modes for telecommunication system, where two types of traffic, i.e. voice and data arrive in Poisson fashion. The server starts service only when N packets are accumulated in the system. The server performs service singly until there are C packets in the system. After then type 2 packets are discarded and all type 1 packets are served in a batch. The arrival rates of packets depend upon the server’s status. The transient state probabilities of system states are obtained by solving a set of linear equations with the help of Laplace Transform technique. Performance indices such as average queue length, expected idle time, and expected busy period are determined. We also investigate the optimal value of threshold parameter N and C after which the server changes the mode of service in order to minimize the expected cost. The numerical illustrations are provided to visualize the effect of various parameters on system performance.

Analysis of the Energy-QoS Tradeoff for Contention-Based Wireless Sensor Networks with Synchronous Wakeup Patterns

To conserve energy, periodic active/sleep dynamics is adopted in wireless sensor networks. At the same time, the QoS guarantees, such as packet delay, packet loss ratio and network throughput need to be satisfied. We develop a finite queuing model for sensor nodes and derive network performance for contention-based wireless sensor networks with synchronous wakeup patterns. Furthermore, the impact of active/sleep duty cycle, time scale and node buffer size on the tradeoff between energy efficiency and QoS guarantees is studied based on the model. Simulation results well match our analytical results and validate the accuracy of our model and approach.

Finite queueing systems—structural investigations and optimal design

We consider the M/M/ K/ S queue as a special but widely applicable finite queueing model. Nevertheless, there exist formulas for various performance measures in the steady state almost nothing is known about first (monotony) and second-order properties (convexity/concavity) of these measures. In the paper we prove such properties. Then an optimisation problem is defined with parameters K and L= S− K as decision variables. Using the properties of the performance measures a simple algorithm to search a solution of the optimisation problem is formulated. Numerical examples round off the investigations.

Performance analysis of an AAL multiplexer with dynamic bandwidth allocation in an IP/ATM environment

In this paper, we present a discrete-time queueing model with a Markov modulated batch Bernoulli process (MMBBP) as a bursty input traffic model of internet protocol packets in order to investigate the performance of a ATM adaptation layer (AAL) multiplexer with a finite buffer and a threshold-based dynamic bandwidth allocation scheme (DBAS). As a deterministic service time, we use the segmentation processing time devoted to a cell payload in the AAL multiplexer. This service time consists of several slot times and varies in line with threshold levels of the buffer contents. In an MMBBP process, the arrivals during a slot time occur as batch Bernoulli processes with a general distribution of batch sizes varying according to the phases of a Markov chain. We obtain the loss probability and the mean delay of an arbitrary packet. We present some numerical results to show the effects of the burstiness and thresholds on the performance of the AAL multiplexer with a DBAS. Scope and purpose The model which we present takes its origin in the research of appropriate traffic management schemes for carrying Internet protocol (IP) traffic on ATM networks. Due to the connection-oriented nature of ATM and unpredictable bursty characteristics of IP traffic, we need some dynamic schemes in the AAL multiplexer of an interworking unit such as a router in order to support a bandwidth allocation algorithm for IP traffic over ATM backbone networks. Discrete-time finite queueing model has gained to describe queueing multiplexer in an ATM environment where time is slotted into one cell transmission time. Recently, many works reveal the bursty nature of packet arrivals to the IP packet multiplexer. Therefore, we focus on a discrete-time finite queueing model MMBBP/D/1/K of the AAL multiplexer with a threshold-based DBAS in order to control the bursty IP traffic transferred to ATM networks. We analyze the presented model by using the classical supplementary variable method in queueing theory. As a result, we obtain the steady-state queue size distribution at an arbitrary time point and the loss probability and the mean delay of an arbitrary packet.

Performance analysis of threshold based bandwidth allocation scheme for IP traffic on ATM networks

The authors analyse a discrete-time based finite queueing model with deterministic service times and a Markov modulated batch Bernoulli process (MMBBP) as a bursty input traffic model in order to investigate the performance of a double threshold based dynamic bandwidth allocation scheme for IP traffic on ATM networks. It is assumed that the segmentation processing time devoted to each cell requires several slot times. In an MMBBP process, the arrivals during a slot time occur as batch Bernoulli processes with the batch size distributions varying according to the phases of a Markov chain. As performance measures, the packet loss probability and the mean packet delay of an arbitrary packet are obtained. Some numerical results are presented to show the performance of the dynamic bandwidth allocation scheme.

On a Single-Server Finite Queuing Model with State-Dependent Arrival and Service Processes

This paper generalizes the M/G/1 queuing process by considering both the arrival and the service rates as being essentially arbitrary functions of the current number of customers in the system, and by assuming, moreover, that the amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. Taking the imbedded Markov chain approach, the paper proposes a method for calculating (1) the limiting probability distribution of the congestion and (2) the expected value of the time needed to complete a service. An expression for the distribution of the waiting time is then given and its first moment deduced.