In this study, we analyze a finite-buffer M/G/1 queueing model with randomized pushout space priority and nonpreemptive time priority. Space and time priority queueing models have been extensively studied to analyze the performance of communication systems serving different types of traffic simultaneously: one type is sensitive to packet delay, and the other is sensitive to packet loss. However, these models have limitations. Some models assume that packet transmission times follow exponential distributions, which is not always realistic. Other models use general distributions for packet transmission times, but their space priority rules are too rigid, making it difficult to fine-tune service performance for different types of traffic. Our proposed model addresses these limitations and is more suitable for analyzing communication systems that handle different types of traffic with general packet length distributions. For the proposed queueing model, we first derive the distribution of the number of packets in the system when the transmission of each packet is completed, and we then obtain packet loss probabilities and the expected number of packets for each type of traffic. We also present a numerical example to explore the effect of a system parameter, the pushout probability, on system performance for different packet transmission time distributions.

In a group-testing method, instead of testing a sample, for example, blood individually, a batch of samples are pooled and tested simultaneously. If the pooled test is positive (or defective), each sample is tested individually. However, if negative (or good), the test is terminated at one pooled test because all samples in the batch are negative. This paper considers a queueing system with a two-stage group-testing policy. Samples arrive at the system according to a Poisson process. The system has a single server which starts a two-stage group test in a batch whenever the number of samples in the system reaches exactly a predetermined size. In the first stage, samples are pooled and tested simultaneously. If the pooled test is negative, the test is terminated. However, if positive, the samples are divided into two equally sized subgroups and each subgroup is applied to a group test in the second stage, respectively. The server performs pooled tests and individual tests sequentially. The testing time of a sample and a batch follow general distributions, respectively. In this paper, we derive the steady-state probability generating function of the system size at an arbitrary time, applying a bulk queuing model. In addition, we present queuing performance metrics such as the offered load, output rate, allowable input rate, and mean waiting time. In numerical examples with various prevalence rates, we show that the second-stage group-testing system can be more efficient than a one-stage group-testing system or an individual-testing system in terms of the allowable input rates and the waiting time. The two-stage group-testing system considered in this paper is very simple, so it is expected to be applicable in the field of COVID-19.

COVID-19 has been spreading all around the world, and threatening global health. In this situation, identifying and isolating infected individuals rapidly has been one of the most important measures to contain the epidemic. However, the standard diagnosis procedure with RT-PCR (Reverse Transcriptase Polymerase Chain Reaction) is costly and time-consuming. For this reason, pooled testing for COVID-19 has been proposed from the early stage of the COVID-19 pandemic to reduce the cost and time of identifying the COVID-19 infection. For pooled testing, how many samples are tested in group is the most significant factor to the performance of the test system. When the arrivals of test requirements and the test time are stochastic, batch-service queueing models have been utilized for the analysis of pooled-testing systems. However, most of them do not consider the false-negative test results of pooled testing in their performance analysis. For the COVID-19 RT-PCR test, there is a small but certain possibility of false-negative test results, and the group-test size affects not only the time and cost of pooled testing, but also the false-negative rate of pooled testing, which is a significant concern to public health authorities. In this study, we analyze the performance of COVID-19 pooled-testing systems with false-negative test results. To do this, we first formulate the COVID-19 pooled-testing systems with false negatives as a batch-service queuing model, and then obtain the performance measures such as the expected number of test requirements in the system, the expected number of RP-PCR tests for a test sample, the false-negative group-test rate, and the total cost per unit time, using the queueing analysis. We also present a numerical example to demonstrate the applicability of our analysis, and draw a couple of implications for COVID-19 pooled testing.

Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1≤n≤K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

We propose a new priority discipline called the strict T-preemptive priority discipline, and derive the waiting time distributions of each class in the strict T-preemptive priority M/G/1 queue. Using this queueing analysis, we evaluate the performance of an opportunistic spectrum access in cognitive radio networks, where a communication channel is divided into time slots, a licensed primary user is assigned to one channel, and multiple unlicensed secondary users may opportunistically exploit time slots unused by the primary user. We also present a numerical example of the analysis of the opportunistic spectrum access where the arrival rates and service times distributions of each users are identical.

  The BMAP/M/N/0 queueing system operating in Markovian random environment is investigated. The stationary distribution of the system is derived. Loss probability and other performance measures of the system also are calculated. Numerical experiments whic

본 논문에서는 통신망의 트래픽 제어를 위한 무한버퍼, 단일 서버와 배치도착과정을 갖는 대기행렬 모형을 고려하였다. 또한 고객 도착 형태와 서비스의 분포는 지수분포를 배치 흐름은 포아송 정상과정 및 배치크기는 기하분포를 따른다고 가정하였다. 서비스를 받기 위해 시스템으로 들어오는 배치의 크기는 시스템의 상태에 따라서 트래픽 제어가 가능하다. 이와 같은 조건에서 시스템에 있는 고객의 수와 배치크기에 대한 결합 확률분포를 분석하였고, 행렬기법을 적용하여 시스

  A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of

  여러 형태의 고객이 외부로부터 포아송과정에 따라 각 대기행렬에 도착하고 정해진 서비스규칙에 따라 해당 서비스를 받은 후 마코비안 확률분포에 따라 시스템을 떠나거나 다른 형태의 고객으로 시스템을 다시 돌아 올 수도 있는 M/G1 대기행렬시스템을 고려한다. 본 연구에서는 기존의 연구 모형을 확장하여 계층적 서비스 규칙을 갖는 우선순위 대기행렬모형을 제시하고 이에 대한 시스템 성능척도를 보다 체계적으로 구할 수 있는 방법을 소개한다. 이를 위하여 먼저 대

Due to the complexity and stochastic nature of automated warehousing system, items are usually queued up at I/O point. We introduce a storage/retrieval policy : dual-command. We present quick approximations to queueing phenomena under these policies. It i