On the stability of queues with the dropping function

In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.

Divide and Conquer: A Hygienic, Efficient, and Reliable Assembly Line for Housekeeping

Problem definition: This work focuses on the hotel housekeeping process. In a field study, a possible channel of disease transmission between consecutive guests in hotel rooms is revealed. In order to prevent the transmission, an innovative assembly-line housekeeping method is developed. Academic/practical relevance: The transmission of infectious diseases during hotel stays (e.g., by touching unclean towels or bed linens) has been reported globally. Under the current COVID-19 pandemic, having contact with saliva or mucus left by an infected person could cause infection. The standard housekeeping process used by the majority of hotels leaves a channel for new towels and bed linens in refreshed rooms to be contaminated by bacteria or viruses from used towels and bed linens. Eliminating the contamination channel and preventing disease transmission are crucial for protecting the health and safety of hotel guests, especially under a disease outbreak such as the current COVID-19 pandemic. Methodology: The research was conducted during a field study at a hotel. To design the assembly-line process, the service time distribution of each housekeeping operational step is characterized using data collected from the practice at hundreds of hotel rooms. An optimization model is proposed to optimize the operation. Through a pilot test, the performance of the assembly-line and the traditional housekeeping methods is compared. Results: The pilot test results show that the assembly-line housekeeping method has the potential to improve not only hygienic standards but also, labor efficiency and service quality (error rate). Managerial implications: The outbreak of the COVID-19 pandemic draws tremendous public attention on disease transmission and public hygiene. The principle of the assembly-line method (i.e., eliminating contamination channels through teamwork operational design) can be applied to not only hotel housekeeping practices but also, many other service settings. It leads to hygienic, efficient, and reliable operations, at no additional cost.

An Efficient Convolution Algorithm for the Non-Markovian Two-Node Cyclic Network

Consider a closed cyclic queueing model that consists of two nodes and a total of M customers. Each node buffer can accommodate all M customers. Node 1 has N ≤ M servers, each having an exponential service time with rate λ . The second node consists of a single server with a general service time distribution function B . . The well-known machine repair model with spares, where a set of identical machines, N , is served by a single repair person, is a key application of this model. This model has several other applications in performance evaluation, manufacturing, computer networks, and in reliability studies as it can be easily used to compute system availability. In this article, we give an efficient algorithm to derive an exact solution for the steady state system size probabilities. Our approach is based on developing an efficient polynomial convolution method to compute the transition probabilities of a birth process over node 2 service times and solving an imbedded Markov chain at node 2 service completion epochs. This is a significant improvement over the exponential algorithm given in an earlier paper. Numerical examples are given to demonstrate the performance of our method.

Analysis of a k-Stage Bulk Service Queuing System with Accessible Batches for Service

In most of the service systems considered so far in queuing theory, no fresh customer is admitted to a batch undergoing service when the number in the batch is less than a threshold. However, a few researchers considered the case of customers accessing ongoing service batch, irrespective of how long service was provided to that batch. A queuing system with a different kind of accessibility that relates to a real situation is studied in the paper. Consider a single server queuing system in which the service process comprises of k stages. Customers can enter the system for service from a node at the beginning of any of these stages (provided the pre-determined maximum service batch size is not reached) but cannot leave the system after completion of service in any of the intermediate stages. The customer arrivals to the first node occur according to a Markovian Arrival Process (MAP). An infinite waiting room is provided at this node. At all other nodes, with finite waiting rooms (waiting capacity cj,2≤j≤k), customer arrivals occur according to distinct Poisson processes with rates λj,2≤j≤k. The service is provided according to a general bulk service rule, i.e., the service process is initiated only if at least a customers are present in the queue at node 1 and the maximum service batch size is b. Customers can join for service from any of the subsequent nodes, provided the number undergoing service is less than b. The service time distribution in each phase is exponential with service rate μjm, which depends on the service stage j,1≤j≤k, and the size of the batch m,a≤m≤b. The behavior of the system in steady-state is analyzed and some important system characteristics are derived. A numerical example is presented to illustrate the applicability of the results obtained.

A Service System with Packing Constraints: Greedy Randomized Algorithm Achieving Sublinear in Scale Optimality Gap

A service system with multiple types of arriving customers is considered. There is an infinite number of homogeneous servers. Multiple customers can be placed for simultaneous service into one server, subject to general packing constraints. The service times of different customers are independent even if they are served simultaneously by the same server; the service time distribution depends on the customer type. Each new arriving customer is placed for service immediately into either an occupied server, that is, one already serving other customers, as long as packing constraints are not violated or into an empty server. After service completion, each customer leaves its server and the system. The basic objective is to minimize the number of occupied servers in steady state. We study a greedy random (GRAND) placement (packing) algorithm, introduced in our previous work. This is a simple online algorithm that places each arriving customer uniformly at random into either one of the already occupied servers that can still fit the customer or one of the so-called zero servers, which are empty servers designated to be available to new arrivals. In our previous work, a version of the algorithm, labeled GRAND(aZ), is considered, in which the number of zero servers is aZ with Z being the current total number of customers in the system and positive a being an algorithm parameter. GRAND(aZ) is shown in our previous work to be asymptotically optimal in the following sense: (a) the steady-state optimality gap grows linearly in the system scale r (the mean total number of customers in service), that is, as c(a)r for some positive c(a), and (b) c(a) vanishes as a goes to zero. In this paper, we consider the GRAND(Zp) algorithm, in which the number of zero servers is Zp, where p < 1 is a fixed parameter, sufficiently close to 1. We prove the asymptotic optimality of GRAND(Zp) in the sense that the steady-state optimality gap is sublinear in the system scale r. This is a stronger form of asymptotic optimality than that of GRAND(aZ).

Simulation modeling of toll plaza operation at the main direction of the intraurban toll road

A large number of toll road projects with a barrier toll collection system are currently being implemented in Russia. Therefore, it seems relevant to study the toll plaza as an element of the transport infrastructure. Insuffi cient attention to the issues of assessing current and predicted intensity on TPscan cause regular traffi c congestions on toll roads. The goal of this study is to build a simulation model that allows to evaluate the capacity of the toll collection point during the operation of the toll road at different traffi c fl ow rates, taking into account the ratio of different types of vehicles and user behavior errors. Visual observation materials are used, the research method is discrete-event simulation of PVP using AnyLogic software, processing of the results is performed in the statistical package R. The toll point (TP) the Western High-Speed Diameter toll road in St. Petersburg, Russia was considered as a case for the study.As a result was build simulation model of TP was developed, taking into account the traffi c specifi cs and user behavior errors. Conducted experiments established the peak traffi c intensities, when traffi c congestion begins to form at the TP, with different ratios of electronic toll collection usage. During the analysis, few cases of service time distribution were considered — from low to high traffi c intensities. Main conclusions of the study: -for the low intensity case, the results of the analysis showed the splitting of the total distribution of the service time into two distributions for different operating modes of toll lanes, — for high intensity, the infl uence of user behavior on service time distribution was revealed, — for each case, the parameters of the gamma laws of service time distribution were determined, — in case of insuffi cient throughput capacity, the TP stops working effi ciently, and service time distribution increases, regardless of the type of payment. Estimated peak hours of TP operation, when there is a potential for congestion at the TP were defi ned. Possible ways of further increase thetoll collection system throughput capacity for the TP were indicated.

Analysis of Steady State Behaviour of Biserial and Parallel Queue Network Model with Batch Arrival

The primary objective of the paper is to analyse a network queue model with two queuing subsystems commonly allied to a single server. The first queue subsystem consists of two biserial servers while the other subsystem consists of three non serial parallel servers. At biserial queueing subsystem, the customers arrive in batches of fixed size from outside the system and individual arrival takes place at parallel subsystem. The input process is poisson and the service time distribution is exponential. Time independent solution and various queue characteristics have been calculated using generating function technique and laws of calculus. Numerical illustration is provided to have clear understanding of the model.

Service Rate and Admission Control in an M/G/1 Queue with State-Dependent Arrival Rates

Admission and service rate control problems in queueing systems have been studied in the literature. For an exponential service time distribution, the optimality of the threshold-type policy has been proved. However, in production systems, the production time follows a general distribution, not an exponential one. In this paper, control of the service speed according to the number of customers is considered. The analytical results of an M/G/1 queue with arrival and service rates that depend on the number of customers in the system, which is called an Mn/Gn/1 queue, are used to compute the performance measure of service rate control. In particular, for the case in which the arrival rates are the same among queue-length intervals, a computation method for deriving stationary distributions is developed. Constant, uniform, exponential, and Bernoulli distributions on the service time are considered via numerical experiments. The results show that the optimal threshold depends on the type of distribution, even if the mean value of the service time is the same. In addition, when the reward rate is small, a case in which a non-threshold-type service rate control policy outperforms all threshold-type policies is identified.

Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution

The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach.