Bulk Service Research Articles

Analytic computation for stationary distributions of D-BMAP/D -MSP(a,b)/1 queueing system

ABSTRACT This paper analyses single server correlated batch arrival and correlated batch service queue with innumerable waiting space in discrete-time. The arrival and service processes are governed by discrete batch Markovian arrival process and discrete Markovian service process with general bulk service rule, respectively. Observing two consecutive random epochs, we construct general structure transition probability matrix and it is then reblocked to the desired M/G/1 structure. The UL-type RG-factorization approach combined with spectral expansion method is adopted to unravel the queue length distribution at random epoch. The relationships are undertaken to obtain the queue length distributions at pre-arrival, outside observer's, intermediate and post-departure epochs. Our most challenging effort is to derive the probability mass functions of waiting time and service batch size for arbitrary customer in an arriving batch. We address the warehouse management process for finished products from dealer to retailer as a potential practical use of our batch queue with correlation in both arrival and service, and provide the effect of our queueing behaviour in this application based on our analytical and computational investigation. Based on the implementation of parametrized numeric experiments with numerous categories, we impart our computational results to validate the analytical findings reported in this investigation.

QUEUING SYSTEM WITH BULK SERVICE AS A MODEL OF SCTP PROTOCOL FUNCTIONING

The article presents the results of developing a model for the Stream Control Transmission Protocol functioning as a queuing system with bulk service. It constructs a graph of states and transitions for deriving linear and differential equation systems regarding the state probabilities. We obtain explicit solutions to analyse the basic SCTP functioning. Keywords: computer network, protocol, probabilistic model, queuing system, bulk service.

Analysis of Batch Arrival Bulk Service Priority Queue with Multiple vacation, Close down, Set up, Differentiate Breakdown and Repair

Analysis of Batch Arrival Bulk Service Priority Queue with Multiple vacation, Close down, Set up, Differentiate Breakdown and Repair

Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation

In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size ′a′ and maximum bulk size ′b′. In the first essential service (FES) completion epoch, if the server fails, with probability ′δ′, then the renewal of the service station is considered. On the other hand, if there is no server failure, with a probability ′1−δ′, then the server switches to a second essential service (SES) in succession. A customer who requires further service as feedback is given priority, and they join the head of the queue with probability β. On the contrary, a customer who does not require feedback leaves the system with a probability ′1−β′. If the queue length is less than ′a′ after SES, the server may leave for a single vacation with probability ′1−β′. When the server finds an inadequate number of customers in the queue after vacation completion, the server becomes dormant. After vacation completion, the server requires some time to start service, which is attained by including setup time. The setup time is initiated only when the queue length is at least ′a′. Even after setup time completion, the service process begins only with a queue length ‘N’ (N > b). The novelty of this paper is that it introduces an essential two-phase bulk service, immediate Bernoulli feedback for customers, and renewal service time of the first essential service for the bulk arrival and bulk service queueing model. We aim to develop a model that investigates the probability-generating function of the queue size at any time. Additionally, we analyzed various performance characteristics using numerical examples to demonstrate the model’s effectiveness. An optimum cost analysis was also carried out to minimize the total average cost with appropriate practical applications in existing data transmission and data processing in LTE-A networks using the DRX mechanism.

Performance study of the M/M(a,b)/1/MWV queuing system with types of breakdowns

Abstract This paper analyses the M/M(a,b)/1/MWV queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter λv which follows Poisson distribution and server provides service in regular busy period with parameter µrb and under the multiple working vacations it provides service with parameter µwv with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as βv 1 and the breakdown during busy state is denoted as βv 2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.

Analysis of Single Server Queueing System with Encouraged Arrival rate of Customers

In this study, we explore a queuing system with a single server that facilitates the arrival of Encouraged consumers while limiting server control. For first-time users, the server in this configuration provides three distinct service types (one by one service, bulk service with an accessible collection, and non-accessible collection). To calculate the predicted number of customers waiting in queue, the likelihood of a steady state, and a system of difference differential equation, the Laplace transform is used. The tabular format is used to display the numerical findings.

The changing adoption behaviors on electric trucks over time during the intention-purchase stage: Insights from freight enterprises’ states and perception features

This study analyzed the possibility and time gap in the adoption of electric trucks during the intention-purchase stage. An online survey was conducted with 980 freight fleets in Zhejiang Province, China in May 2021. The survival analysis model was employed to integrate the time variable with the probability of purchase, and various state and perception features that significantly influenced adoption behaviors were identified. The predictive performance of the model was assessed using the C-index and by comparing the results with actual purchase data. The findings indicated that positive state factors effectively reduce the time to purchase during the intention-behavior stage, while negative perception factors substantially decrease the ultimate purchase probability. Specifically, enterprises offering bulk services experienced a 10% increase in their purchase probability during the second year. Conversely, a negative perception of overall profit and empty-running reduction resulted in a 59.5% and 68.5% reduction in the purchase probability, respectively. The model demonstrated good predictive accuracy, particularly for short time periods of less than two years. This research has important implications for mitigating bias in intention survey data, providing policymakers with new incentives derived from the business environment, and facilitating the transition to electric trucks in freight transportation for cleaner production.

A novel data-driven patient and medical waste queueing-inventory system under pandemic: a real-life case study

It is necessary to control patient congestion in medical centers during pandemics where medical demand grows rapidly. Also, managing generated medical waste is critical since pandemic waste can be a source of disease spread. Although some researchers have studied healthcare optimization in medical systems, there is still a lack of models simultaneously managing congestion in medical centers integrated with waste management using a new application of queueing systems. The model is also the first to use a data-driven method to develop a mathematical model of healthcare and waste management. To fill these gaps, this paper develops a multi-shift mathematical model to manage the congestion in the medical center and medical waste during the pandemic. To this aim, patients are categorized using machine learning algorithms at first. Then, the number of outpatients and inpatients, as well as medical waste, is modeled as a Markovian healthcare waste queueing-inventory system (HWQIS) using a bulk service queueing model. A case study based on the Covid-19 pandemic is applied after the model has been validated using twelve test problems. By determining the optimal size of waste packages, vehicle capacity, and the number of servers, we minimized the patients waiting time and reduced waste accumulation.

A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following a Poisson process and the server operates under (a,b)-bulk service rule. The queueing system has a finite-buffer capacity ‘N’ excluding the batch in service. The service-time distribution of batches follows a general distribution, which is independent of the arrival process. We first develop an alternative approach of obtaining the probability distribution for the queue length at a post-departure epoch of a batch and, subsequently, the probability distribution for the queue length at a random epoch using an embedded Markov chain, Markov renewal theory and the semi-Markov process. The waiting-time distribution (in the queue) of a random customer is derived using the functional relation between the probability generating function (pgf) for the queue-length distribution and the Laplace–Stieltjes transform (LST) of the queueing-time distribution for a random customer. Using LSTs, we discuss the derivation of the probability density function of a random customer’s waiting time and its numerical implementations.

Analysis of bulk service queuing system with rework, unreliable server, resuming service and two kinds of multiple vacation

In this paper, we discuss a batch arrival bulk service queue with rework for the faculty item, possibility of breakdown, repair, and two kinds of multiple vacation with different threshold policy. The server serves the remaining service after repair completion. This type of queuing model has a lot of applications in the manufacturing/ production industries. Performance measures and stability conditions are obtained. Numerical illustrations are made to examine the validity of analytical results.

Performance analysis of an infinite-buffer batch-size-dependent bulk service queue with server breakdown and multiple vacation

<p style='text-indent:20px;'>In several manufacturing systems, server's breakdown is a common phenomenon for which renovation of the service station is required and has a definite effect on the system. The server's vacation is a significant tool to deal with the systems where a common server is shared by several users. The principal goal of this paper is to analyze a batch-service queueing model with server's breakdown, multiple vacations and batch-size-dependent service time. To be more precise, the center of attention is on the queue length together with server content distribution for which we obtain the bivariate probability generating function using supplementary variable technique. Server content distribution is very worthy for the manufacturing systems. The probabilities have been extracted and used to acquire the arbitrary epoch probabilities. In order to upgrade the qualitative aspects of the concerned model, diverse numerical results and graphical observations are illustrated.</p>

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

The orthodox way of tile printing results in mulish production. To tame this, digital inkjet printing technology was imposed. In this article, a mathematical prototype is designed exclusively for the tile printing wing. The various plants coming under printing are correlated to the proposed prototype. The article throws light on the functioning of the prototype. The prototype turns up subservient to bulk service queue models with two types of vacations. The prototype is resolved under the supplementary variable technique. The prototype with peculiar conditions is proved to be the existing model. Anticipated line distance, awaited active duration, awaited standby time, and expected idle period were computed. Thus, the total average cost is acquired for diverse vacation values. The main intention of the pattern is to downside the total average cost.

Analysis of batch size-dependent bulk service queue with multiple working vacation

ABSTRACT The present article analyses an infinite buffer batch size-dependent bulk service queue with multiple working vacation (MWV). The customer's arrival pattern follows the Poisson process, and they get the service in batches according to the general bulk service (GBS) rule in regular period (RP) as well as in working vacation period (WVP). After one service in RP, if the queue size is greater or equal to the lower threshold of the GBS rule, then the server performs the service in RP, otherwise, it starts the working vacation (WV) following exponential vacation time distribution. During the WVP, the server serves the customers in batches (if any) at a lower service rate than the usual service rate. The service time in the RP as well as in WVP is generally distributed. At an arbitrary epoch, the joint probabilities of the queue size and batch size with the server in RP as well as in WVP have been obtained using the supplementary variable technique (SVT) and the bivariate generating function method. Finally, some numerical observations are presented to enhance the applicability of the analytical results.

Analysis of Flexible Batch Service Queueing System to Constrict Waiting Time of Customers

When the required number of customers is available in the general bulk service (GBS) queueing system, the server begins service. Otherwise, the server will remain inactive until the number of consumers in the queue reaches that minimum required number. Customers that have already come must wait throughout this time, regardless of their arrival time. In some circumstances, like specimens awaiting testing in a clinical laboratory or perishable commodities awaiting delivery, it is necessary to finish services before the expiration date. It might only be achievable if consumers’ waiting times are kept under control. As a result, the flexible general bulk service (FGBS) rule is developed in this article to provide flexibility in batching. The effectiveness of FGBS implementation has been demonstrated using two examples: a clinical laboratory and a distribution center. To justify the suggested model, a simulation study and numerical illustration are provided.

Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates

In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.

Analysis of a Batch arrival Bulk Service Queue with Two Choice of Service Multiple Vacations Restricted Admission and Closedown Time

Analysis of a Batch arrival Bulk Service Queue with Two Choice of Service Multiple Vacations Restricted Admission and Closedown Time

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.

An updatable and comprehensive global cargo maritime network and strategic seaborne cargo routing model for global containerized and bulk vessel flow estimation

The global maritime system provides the backbone of logistics operations for global supply chains and international trade. This paper aims to develop a unifying global network representation and strategic, system-wide decision model, the Strategic Cargo Routing Model, incorporating both liner and bulk shipping markets to estimate real-world traffic flows and study traffic patterns at the global scale. Specifically, taking a shipper's perspective, containerized and bulk movements are jointly modelled within a mixed-integer linear program that includes inbound, outbound, and transshipment cargo flows at ports. An iterative approach that combines heuristic Gradient Descent and Relax-and-Fix Decomposition methods is proposed for the calibration and solution of the Strategic Cargo Routing Model over a proposed joint liner and bulk services Global Cargo Shipping Network representation. The Global Cargo Shipping Network contains 161 seaports covering 52 countries. It is created from updatable, publicly available, data sources, and all data needed for the network representation are made available. Sufficient network details, as well as data sources and methods for extracting needed inputs, are given to allow others to use and update the network. Using the developed maritime network, mathematical model and calibration-solution methodology, 2018 global maritime traffic flow patterns were estimated. The estimates were found to achieve a 91% fit overall to real-world average annual port throughputs. This strategic model provides support to evaluate future, real-world, worldwide changes, such as increased seaborne trade demand, new routes, shipping infrastructure expansion, and transport policies.

Analysis of customer's impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacations

In this investigation, we analyse the customer's impatience on unreliable bulk queueing system with two types of vacation. Depending upon the length of queue, the server is permitted to take two types of vacation called type I vacation and type II vacation. The server is possibly affected by breakdowns and takes considerable time for setup before the repair begins to start. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. It could be assumed that the arriving units may be balked from the system when the server is on vacation (type I or type II). By incorporating the supplementary variables technique, the probability generating function of the queue size at an arbitrary and departure time epoch for the designed queueing system are derived. Finally, the stability condition, some performance measures, particular cases are obtained with appropriate numerical illustrations and graphical presentation.

Analysis of infinite buffer general bulk service queue with state dependent balking

This paper investigates the effect of impatient phenomena of the arriving customers in a bulk service queue, where inputs are flowing into the system according to the Poisson process and are served in groups according to the 'general bulk service' (GBS) rule. The service time of a group of customers follows exponential distribution. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size and status of the server, i.e., whether server is busy or idle. The steady state joint probability distribution of the number of customers in the queue as well as with the server is obtained by using the probability generating function method, which is based on the roots of the characteristic equations formed using probability generating function for steady state joint probabilities. Finally, various performance measures, such as, average queue length, average waiting time, probability that the server is busy, average queue length when server is busy, etc., have been obtained. The paper ends with several numerical discussions to demonstrate the effect of certain model parameters on the key performance measures.