The Analysis, Optimization, and Simulation of a Two-Stage Tandem Queueing Model with Hyperexponential Service Time at Second Stage

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.

In real-time wireless control systems, the freshness of information is crucial since performance highly depends on timely exchange of information between the plant and the controller. In this study, the age metric, Age of Control Process (AoCP), is proposed for real-time wireless control systems which is different from traditional Age of Information (AoI). The First Generate First Serve (FGFS) M/M/1/1 → M/M/1/1 tandem queue model is considered to present a closed form expression for computation of AoCP and testbed environment is employed for the analysis of AoCP measure. Our experiment results show that FGFS M/M/1/1 → M/M/1/1 queuing model is suitable to represent real-time control systems. In addition, the proposed definition provides closer results to the experiment results when compared with the traditional AoI definition. To the best of our knowledge, this is the first study that conducts information freshness measurements on real-time control testbed.

This research aims to determine the queue model on a motorcycle parking area at Jember Universityand its performance measures. The data collection method in this research uses the observation method. Data taken are the number of arrivals, the number of departures, and service time. To get arrival distribution and service time distribution use mathematical calculation and Kolmogorov-Smirnov Test with SPSS Statistics. After arrival distribution and service time distribution are known, then using Kendall Notation rule to get queue model. Formula derivation and POM-QM for Windows are used to obtain performance measurement values in the queue model. After getting the data needed through observation, then analysedtaht data to determine the value of arrival rate and service rate, then the data is reanalysed to find out the data obtained has been steady-state. This research is known that steady-state, so that distribution test can be done, with the result that the arrival distribution was Poisson distribution and the service time distribution was Exponential distribution. In modelling the queue Kendall Notation is required. It’s used to clarify how the queue system reviewed works and is modelled. Based on the results of data analysis in this research, the queue model obtained was (M/M/1):(FIFO/∞/∞).

In this paper, we consider two queueing models. Model I is on a single-server queueing system in which the arrival process follows MAP with representation D = (D0,D1) of order m and service time follows phase-type distribution (β, S) of order n. When a customer enters into service, a generalized Erlang clock is started simultaneously. The clock has k stages. The pth stage parameter is θp for 1 ≤ p ≤ k. If a customer completes the service in between the realizations of stages k1 and k2 (1 < k1 < k2 < k) of the clock, it is a perfect one. On the other hand, if the service gets completed either before the kth1 stage realization or after the kth2 stage realization, it is discarded because of imperfection. We analyse this model using the matrix-geometric method. We obtain the expected service time and expected waiting time of a tagged customer. Additional performance measures are also computed. We construct a revenue function and numerically analyse it. In Model II, a single server queueing system in which all assumptions are the same as in Model I except the assumption on service time, is considered. Up to stage k1 service time follows phase-type distribution (α′ , T′) of order n1 and beyond stage k1, the service time follows phase type distribution (β′ , S′) of order n2. We compare the values of the revenue function of the two models

Algorithm for computing the queue length distribution at various time epochs in DMAP/G(1, a, b)/1/N queue with batch-size-dependent service time

Queuing models need well defined knowledge on arrivals and service times. However, in real applications, because of some measurement errors or some loss of information, it is hard to achieve deterministic knowledge. Non-deterministic knowledge interferes or complicates analysis of the queuing model. Additionally, when the customers are asked about their impressions on waiting times or service times, mostly the answers are linguistic expressions like "I waited too much", "service was fast", and that the responses are. Linguistic statements and ill defined data make the sense of imprecision in the model. In this study, arrivals and service times are defined as fuzzy numbers in order to represent this imprecision. Fuzzy multi-channel queuing systems and membership functions are introduced in defining the arrivals and service times. Besides, a new membership function based on a probability function is studied. Fuzzy queuing characteristics are calculated via different membership functions and the results are compared on simulations. Among models it is found that, Generalized Beta Distribution membership function is the one that minimized the queuing characteristics.

Database systems allow quick creation of performance problems. The goal of database systems is to allow the computer-illiterate to write complex and complete applications. It is the job of the syst...

The analysis of system performance measures is fairly simple if there is only one or several channels with identical service times and arranged in parallel with exponentially distributed inter arrival time of packets and service time. However, heterogeneous multiple channels often occur in practice and here the channels have different service times. It is therefore useful to be able to calculate the performance measures of such systems. We shall take an exact analytical model of the asymmetric data network node and assume that the arrival process is Poisson of two priority flows with different rates and two channels with different service times distributed exponentially and in case with determine service time. In symmetric queuing systems, the response time depends only on whether an arrival message finds some free channel. An asymmetric multiple channel system differs since which of the channels processes the message. It is very important to take analysis of different strategies for selecting a free channel. In a system with heavy traffic there is usually all channels are occupied and therefore a channel selection strategy is not so efficient. The transmission order is from high-priority packet to low-priority packet. Two priority packets queues share a limited size single buffer. The each priority packet is dropped if the queue length exceeds a capacity of buffer. Network node performance measures such as packet losses, packet delay, channel utilization are evaluated by means of analytical and simulation models. Some calculated system performance measures results are presented in figures.

With the proliferation of the Internet-of-things (IoT), there is an undeniable consensus that cellular LTE networks will have to support a dramatically larger number of uplink connections. This is true since most of the devices to be added incur machine-type communications which is dominantly upstream. Can current LTE network withstand this challenge? To answer this question, the joint performance of random access process and the uplink data transmission should be investigated. These two problems have been classically treated in the literature in a disjoint fashion. In this paper, they are jointly analyzed as an inseparable couple. To do that, a tandem queuing model is adopted whereby devices are represented as spatially interacting queues. The interaction between queues is governed by the mutual inter-cell and intra-cell interference. To that end, a joint stochastic geometry and queueing theory model is exploited to study this problem and a spatiotemporal analytical model is developed accordingly. Network stability and scalability are two prime performance criteria for performance assessment. In light of these two criteria, the developed model is poised to offer valuable insights into efficient access and resource allocation strategies.

This paper investigates an energy efficiency (EE) and delay aware user association problem in millimeter wave (mmWave) downlink networks, in which the wire backhaul links are replaced by the wireless backhaul links to transmit traffic data. To characterize the mmWave network delay performance, the queue theory is adopted and an M/M/1 tandem queuing model is introduced to capture the data transmission latency over mmWave backhaul links and access links. Besides, in order to measure the network EE and delay performance simultaneously, a novel EE-delay aware utility function is constructed and the user association problem is formulated. It is proved that the formulated problem is NP-hard. To solve it, one many-to-one matching game is reformulated and a two-steps user association algorithm is proposed. Simulation results show that the proposed association scheme can obtain significant utility improvement, achieving up to 21% gains compared with the classic association schemes. Moreover, the proposed scheme also demonstrates its superiority on load balancing management in mmWave backhaul networks.

This paper provides two different discrete-time finite-buffer queueing models of the G 1 [X] +G2/D/1/s-type for modelling CAC in ATM. In the G 1 [X] +G2-input, G1 and G2 produce (correlated) interarrival times and the independent r.v. X generates the size of the batch arriving, when G1 produces an arrival. Thus, this model represents the situation, when a new connection (G2) is admitted, i.e. superimposed to already existing traffic (G 1 [X] ) in an ATM-switch. The first model -given in detail here- is based on Neuts’ M/G/1-type paradigm, and allows the solution of the queueing model for a DBMAP+DMAP input including the DMAP 1 [X] +DMAP2 case (also for a general service process). Per-stream probability functions (p.f.’s) of the occupancy and loss probabilities can be computed. The second model is based on the unfinished work and allows to compute per-stream loss probabilities, occupancy and waiting-time p.f.’s, as well as, for stream 2, an exact value of the conditional loss probability that given a cell of stream 2 is lost, the next cell of stream 2 is also lost. Since the DMAP 1 [X] +DMAP2-input can be handled by both methods, an analytical validation of the results is possible, which typically only differ in the last 4 of 16 figures (using double-precision-numbers in a C-program). Both models allow service times higher than the time-unit, which is necessary for a correct description of a multiplexer’s behaviour, when the output line is slower than the input lines. Numerical results show that positive correlation in one stream can have a significant negative influence on QOS parameters of both streams so that effective bandwidth does better than sigma rule, since it inherently carries some estimate of correlation.

In this system we consider a batch arrival Poisson input with two phases of heterogeneous service with random feedback in each servivce. The first phase of service is essential for all customers, but with a probability tagged customer chose second phase, feedback to tail of original queue or leave the system. Also, after completion of the second phase, with a probability the customer leaves the system, or feedback to tail of original queue. At each service completion epoch, the server may apt to take a vacation with a probability or continue to be available in the system for the next service. The service times are assumed to be general. The vacation period of the server has two heterogeneous phases with Coxian-2 distribution. The vacation times are assumed to be general. When the server goes for vacation, service become unavailable and customers may decide to renege at each vacation times. We assume reneging follow exponential distribution. All stochastic processes involved in this system (service and vacation times) are independent of each other. We derive the PGF’s of the system and by using them the performance measures are obtained. Some numerical approch are examined the validity of results.

The advent of multimedia applications over wireless networks has necessitated the need for high data rates and a reliable communication over dynamic wireless links. Adaptive Modulation and coding (AMC), Automatic Repeat re-Quest (ARQ) and Forward Error Correction (FEC) have been widely used to overcome the time varying nature of these links and consequently enhancing their performance. The number of packets served per Coherence Time Interval (CTI) when AMC is employed is a function of the quality of the received Signal-to-Noise Ratio (SNR) in that CTI. Since the SNR is variable, the packet/message service time for multi-rate systems is variable. Consequently, when realistic traffic arrivals (random length messages) are considered in multi-rate systems, coupled with the assumption that the transitions from one CTI to the next are Markovian, the queue service process non-Markovian because the message may take more than one CTI to transmit/serve. In this paper, we derive the first and second moments of/and the service time distribution of the modified M/G/1 queuing model that employs AMC herein referred to as M/Gc/1 for TDMA systems over Nakagami-m fading channel. Geometrically distributed message lengths with fixed packet lengths are considered, whose arrivals are Markovian. However, individual packet service times are correlated and affects overall message service time which subsequently determines the delay experienced by a message in a queue awaiting transmission/service.

In future high-speed communication, it is anticipated that cases dealing with fixed-length data will increase. Therefore, a traffic analysis for constant-service-time models is needed. In this paper, a multiserver queuing model M/D/s/N for finite capacity in the system and constant service time is treated. By discrete approximation, its steady-state analysis is attempted. In this analysis, the state at each discrete time step chosen at a constant interval of about 1/10 of the service time is defined by the number of calls in the system and the residual service time for each server. By considering the state transition probability within this time, linear simultaneous equations in the state variables for the previous and next discrete time steps are solved to derive the steady-state probability. In the calculation of the state transition probability, we assume that the departures and arrivals of calls are approximately uniformly distributed. The approximate numerical results are compared with high-precision simulation results as well as with those obtained by applying an existing approximation on M/D/s/N to a constant service time. It is shown that the calculated steady-state probability generally has good accuracy. © 1999 Scripta Technica, Electron Comm Jpn Pt 1, 82(6): 26–33, 1999

We analyze a discrete-time queueing model where two types of customers, each having their own dedicated server, are accommodated in one single FCFS queue. Service times are deterministically equal to s≥1 time slots each. New customers enter the system according to a general independent arrival process, but the types of consecutive customers may be nonindependent. As a result, arriving customers may (or may not) have the tendency to cluster according to their types, which may lead to more (or less) blocking of one type by the opposite type. The paper reveals the impact of this blocking phenomenon on the achievable throughput, the (average) system content, the (average) customer delay and the (average) unfinished work. The paper extends the results of earlier work where either the service times were assumed to be constant and equal to 1 slot each, or the customers all belonged to the same class. Our results show that, in case of Poisson arrivals, for given traffic intensity, the system-content distribution is insensitive to the length (s) of the service times, but the (mean) delay and the (mean) unfinished work in the system are not. In case of bursty arrivals, we find that all the performance measures are affected by the length (s) of the service times, for given traffic intensity.