Two identical communication channels in series with a finite intermediate buffer and overflow

The performance of an ATM switch of a space division architecture with finite FIFO output buffer is considered. The input traffic is modeled by identical Bernoulli processes. The presented analytical approach is based on a queueing model which describes the finite queue occupancy distribution. The evaluation of the cell loss and cell mean delay is compared with previously presented analytical results. It is found that the presented simple model is suitable for determining the finite buffer effect on the ATM network performance in spite of its simplicity and its analytical tractability. An asymptotic relation is obtained between the offered load and the buffer size that gives a constant cell loss behavior. Moreover, the outstanding physical meaning of the presented procedure gives a deep insight into the ATM switch performance parameters as to the network offered load and the switch buffer capacity.

Tandem queues constitute a fundamental structure of queueing networks. However, exact queue times in tandem queues are notoriously difficult to compute except for some special cases. Several approximation schemes that are based on mathematical assumptions that enable approximate analyses of tandem queues have been reported in the literature. This article proposes an approximation approach that is based on observed properties of the behavior of tandem queues: the intrinsic gap and intrinsic ratio. The approach exploits the nearly linear and heavy-traffic properties of the intrinsic ratio, which appear to hold in realistic production situations. The proposed approach outperforms existing approximation methods across a broad range of examined cases. It is also demonstrated that the proposed approach has the potential when applied to historical data to achieve accurate mean queue time estimates in practical production environments. [Supplemental materials are available for this article. Go to the publisher's online edition of IIE Transactions to view the supplemental file.]

To facilitate the development of Internet of Things (IoT) applications, numerous middleware protocols and APIs have been introduced. Such applications built atop reliable or unreliable protocols and they expose different characteristics. Additionally, with regard to the application context (e.g., emergency response operations), several Quality of Service (QoS) requirements must be satisfied. To study QoS in IoT applications, the provision of a generic performance analysis methodology is required. Queueing network models offer a simple modeling environment, which can be used to represent IoT interactions by combining multiple queueing model types for building queueing networks. The resulting networks can be used for performance analysis through analytical or simulation models. In this paper, we present several types of queueing models that represent different QoS settings of IoT interactions, such as intermittent mobile connectivity, message drop probabilities, message availability/validity and resource constrained devices. Using MobileJINQS, we simulate our models demonstrating the significant effect on response times and message success rates when varying QoS settings.

This paper deals with the development and analysis of K-node series and parallel queueing model with load dependent service rates. Here it is assumed that the customers arrive to the initial queue and waiting line for service. After completing the service at first service station they may join one of the (K-1) queues which are parallel and connected to first queue in series. After getting service from the service station they leave the system. Here it is assumed that the service rates in each service station are dependent on number of customers in the queue connected to it .The arrival and service completions in each queue are assumed to follow Poisson processes. Using difference-differential equations the joint probability function of number of customers in each queue are derived. The system performance measures such as average number of customers in each queue ,throughput of each service station ,the probability of idleness of each server ,the waiting time of customer in each queue are derived explicitly. The sensitivity of the model with respect to parameters are analysed through numerical illustration. It is observed that the state dependent service rates has significant influence on performance measures. This model also includes the earlier models as particular cases for specific values of the parameters. This model is useful in analysing the communication networks , transportation systems ,production processes and cargo handling.

Cell loss probability is a critical performance criterion that will be encountered in satisfying the needs of ATM services. To enforce dynamic control on the finite buffer in an ATM switch, it is desirable that multiple loss priority classes can be supported to accommodate diverse connection-levels as well as cell-level loss requirements of users. However, very little work has appeared in literature in the study of controlling cell loss probabilities with multiple priority classes. In this paper we conduct a thorough analysis of a generalized space priority control scheme, the Partial Buffer Sharing scheme, to manage optimally the finite shared buffer system. We develop an analytical queuing model to characterize accurately the system, and present efficient optimization procedures that are capable of finding the optimal loss thresholds to maximize the system admissible load. We verify the optimization procedures, demonstrate the resource efficiency improvement and evaluate the impact of given traffic conditions and cell loss criteria by numerous numerical examples. The study produces a feasible and attractive means to support different grades of loss probabilities with a minimum hardware cost and also to provide a better control on the delay introduced during cell buffering.

Analysis of Packet Switching Communication Networks with Finite Buffers

Queueing models can be used to evaluate the performance of manufacturing systems. Due to the emergence of cluster tools in contemporary production systems, proper queueing models have to be derived to evaluate the performance of machines with complex configurations. Job cascading is a common structure among cluster tools. Because of the blocking and starvation effects among servers, queue time analysis for a cluster tool with job cascading is difficult in general. Based on the insight from the reduction method, we proposed the approximate model for the mean queue time of a cascading machine subject to breakdowns. The model is validated by simulation and performs well in the examined cases.

We present theoretical models and numerical results for performance of a multiprocessor network modeled as a ring and as a 2-dim wraparound square lattice of nodes with local processors that generate messages with rate λ per clock cycle and two or, respectively, four output ports/buffers. Two different models are considered. One assumes that the generation rate of a node depends on the intensity of the flow of arriving messages. The other model considers networks with limited buffers. The average queue lengths and average latency are obtained. The results show that the model of independent queues, which is valid for networks with homogeneous activity and infinite buffers, is not applicable, which violates the Jackson theorem.

Queueing models provide a useful tool for predicting the performance of many service systems including computer systems, telecommunication systems, computer/communication networks and flexible manufacturing systems. Traditional queueing models predict system performance under the assumption that all service facilities provide failure-free service. It must, however, be acknowledged that service facilities do experience failures and that they get repaired. In recent years, it has been increasingly recognized that this separation of performance and reliability/availability models is no longer adequate. An exact steady-state queueing analysis of such systems is considered by several authors and is carried out by means of generating functions, supplementary variables, imbedded Markov process and renewal theory, or probabilistic techniques [1,2,7,8]. Another approach is approximate, in which it is assumed that the time to reach the steady-state is much smaller than the times to failures/repairs. Therefore, it is reasonable to associate a performance measure (reward) with each state of the underlying Markov (or semi-Markov) model describing the failure/repair behavior of the system. Each of these performance measures is obtained from the steady-state queueing analysis of the system in the corresponding state [3,5]. Earlier we have developed models to derive the distribution of job completion time in a failure-prone environment [3,4]. In these models, we need to consider a possible loss of work due to the occurrence of a failure, i.e., the interrupted job may be resumed or restarted upon service resumption. Note that the job completion time analysis includes the delays due to failures and repairs. The purpose of this paper [9] is to extend our earlier analysis so as to account for the queueing delays. In effect, we consider an exact queueing analysis of fault-tolerant systems in order to obtain the steady-state distribution and the mean of the number of jobs in the system. In particular, we study a system in which jobs arrive in a Poisson fashion and are serviced according to FCFS discipline. The service requirements of the incoming jobs form a sequence of independent and identically distributed random variables. The failure/repair behaviour of the system is modelled by an irreducible continuous-time Markov chain, which is independent of the number of jobs in the system. Let the state-space be {1,2, …, n }. When the computer system is in state i it delivers service at rate r i ≥ 0. Furthermore, depending on the type of the state, the work done on the job is preserved or lost upon entering that state. The actual time required to complete a job depends in a complex way upon the service requirement of the job and the evolution of the state of the system. Note that even though the service requirements of jobs are independent and identically distributed, the actual times required to complete these jobs are neither independent nor identically distributed, and hence the model cannot be reduced to a standard M/G/ 1 queue [8]. As loss of work due to failures and interruptions is quite a common phenomenon in fault-tolerant computer systems, the model proposed here is of obvious interest. Using our earlier results on the distribution of job completion time we set up a queueing model and show that it has the block M/G/ 1 structure. Queueing models with such a structure have been studied by Neuts, Lucantoni and others [6]. We demonstrate the usefulness of our approach by performing the numerical analysis for a system with two processors subject to failures and repairs.

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process. Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue. In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

Due to the non-stop and rapid spreading of virus pandemics all over the world, traditional healthcare monitoring capabilities of hospitals and/or medical centers are under a severe over-load. Modern computing infrastructures with the harmony of various layers of computing paradigms (e.g., cloud/fog/edge computing) for healthcare monitoring are apparently the essential computing backbone that help access and process instantly the medical data of every single patient at the very edge of the healthcare system to combat with global or regional virus contagion. Previous studies proposed different computing system architectures for healthcare monitoring but few works considered the evaluation of pure performance of medical data transmission in a comprehensive manner. In this paper, we proposed an M/M/c/K queuing network model for the performance evaluation of an Internet of Healthcare Things (IoHT) infrastructure in association with a three layer cloud/fog/edge computing continuum. The model considers a life cycle of medical data from body-attached IoT sensors in edge layer all the way to local clients (e.g., local medical doctors, physicians) through fog layer and to remote clients (e.g., medical professionals, patient’s family members) through cloud layer. Furthermore, we also explore the impact of the alteration in system configuration and computing capability of computing layers in two scenarios on various performance metrics. Critical performance metrics related to quality of service are evaluated in a comprehensive manner, such as (i) mean response time of medical data transmission to fog (local) clients and to cloud (remote) clients, (ii) utilization of cloud/fog/edge computing layers, (iii) service throughput, (iv) number of medical messages in a period of time, and (v) drop rate. The simulation results pinpoint bottle-neck parameters and configurations of the IoHT infrastructure’s system architecture in relation to the frequency of medical data collection for health check of patients. Thus, the findings of this study can help improve medical administration in hospitals and healthcare centers and help design computing infrastructures in accordance for medical monitoring in the severe circumstances of virus pandemics.

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

Due to the analytical intractability of general tandem queues, we develop methods to quantify the dependence among servers through simulation. Dependence is defined by the contribution queue time at each server, and contribution factors are developed based on the insight from Friedman's reduction method and Jackson networks. In a tandem queue, the dependence among stations can be either diffusion or blocking, and their impact depends on the positions relative to the bottlenecks.

Active Queue Management (AQM) algorithm, as a typical router based congestion control strategy, has been the focus of researchers in the past few years and widely used in congestion control. There are a few drawbacks such as large queuing delay and queue jitter, which cause data retention drop and oscillation. It means that the existing AQM algorithms under high bandwidth can not meet the Quality of Service (QoS) requirements. This paper presents a new algorithm based on the traditional BLUE algorithm and M/M/1/N queuing model which is called QBLUE. Empirical simulations with various experiment data analysis have demonstrated that the prompted new algorithm can reduce the packet dropping rate, increase bandwidth utilization and stabilize the queue length.

The simulation model of the photonic switch designed for optical packet switching networks is presented in this paper for the first time. At first the scheme and the algorithm of operating the photonic switch are considered. Then the simulation model implemented as the program written in Python is proposed. This program reproduces the process of functioning of the considered photonic switch. The expressions for finding the time of packet transmission are presented in the work. They are used in the program and influence on output data such as buffer size and time to wait for a packet in the queue. The dependences of the optical buffer size on the throughput of the communication channel and load are presented in numerical results section. The results of 16×16 photonic switch simulation are considered in this section as the example. For this switch average value of maximum buffer size in dependence on input load and two different throughputs of communication channels 1Tbps and 100Gbps has been calculated. The optical packet length has been 1500 bytes.