scholarly journals Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
Achyutha Krishnamoorthy ◽  
Anu Nuthan Joshua ◽  
Dmitry Kozyrev
Keyword(s):  
Markov Chain ◽  
Idle Time ◽  
Inventory System ◽  
Batch Size ◽  
Service Process ◽  
Batch Service ◽  
First Order ◽  
Order Markov Chain ◽  
Batch Sizes ◽  
Number Of Customers

A single-server queuing-inventory system in which arrivals are governed by a batch Markovian arrival process and successive arrival batch sizes form a finite first-order Markov chain is considered in this paper. Service is provided in batches according to a batch Markovian service process, with consecutive service batch sizes forming a finite first-order Markov chain. A service starts for the next batch on completion of the current service, provided that inventory is available at that epoch; otherwise, there will be a delay in starting the next service. When the service of a batch is completed, the inventory decreases by 1 unit, irrespective of batch size. A control policy in which the server goes on vacation when a service process is frozen until a quorum can initiate the next batch service is proposed to ensure idle-time utilization. During the vacation, the server produces inventory (items) for future services until it hits a specified level L or until the number of customers in the system reaches a maximum service batch size N, with whichever occurring first. In the former case, a server stays idle once the processed inventory level reaches L until the number of customers reaches (or even exceeds because of batch arrival) a maximum service batch size N. The time required for processing one unit of inventory follows a phase-type distribution. In this paper, the steady-state probability vector of this infinite system is computed. The distributions of inventory processing time in a vacation cycle, idle time in a vacation cycle, and vacation cycle length are found. The effect of correlation in successive inter-arrival times and service times on performance measures for such a queuing system is illustrated with a numerical example. An optimization problem is considered. The proposed system is then compared with a queuing-inventory system without the Markov-dependent assumption on successive arrivals as well as service batch sizes using numerical examples.

Optimal control of batch service queues with switching costs

1976 ◽  
Vol 8 (1) ◽  
pp. 177-194 ◽  
Author(s):  
Rajat K. Deb
Keyword(s):  
Optimal Level ◽  
Fixed Number ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Sizes ◽  
Batch Service Queues ◽  
Number Of Customers

We consider a batch service queue which is controlled by switching the server on and off, and by controlling the batch size and timing of services. These batch sizes cannot exceed a fixed number Q, which we call the service capacity. Costs are charged for switching the server on and off, for serving customers and for holding them in the system. Viewing the system as a semi-Markov decision process, we show that the policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the following form: at a review point if the server is off, leave the server off until the number of customers x reaches an optimal level M, then turn the server on and serve min (x, Q) customers; and when the server is on, serve customers in batches of size min(x, Q) until the number of customers falls below an optimal level m(m ≦ M) and then turn the server off. An example for computing these optimal levels is also presented.

Optimal control of batch service queues with switching costs

1976 ◽  
Vol 8 (01) ◽  
pp. 177-194 ◽  
Author(s):  
Rajat K. Deb
Keyword(s):  
Optimal Level ◽  
Fixed Number ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Sizes ◽  
Batch Service Queues ◽  
Number Of Customers

We consider a batch service queue which is controlled by switching the server on and off, and by controlling the batch size and timing of services. These batch sizes cannot exceed a fixed number Q, which we call the service capacity. Costs are charged for switching the server on and off, for serving customers and for holding them in the system. Viewing the system as a semi-Markov decision process, we show that the policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the following form: at a review point if the server is off, leave the server off until the number of customers x reaches an optimal level M, then turn the server on and serve min (x, Q) customers; and when the server is on, serve customers in batches of size min(x, Q) until the number of customers falls below an optimal level m(m ≦ M) and then turn the server off. An example for computing these optimal levels is also presented.

Online to offline social interaction on gaming motivations

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wei-Lun Chang ◽  
Li-Ming Chen ◽  
Yen-Hao Hsieh
Keyword(s):  
Markov Chain ◽  
Online Games ◽  
Online Gaming ◽  
Online Game ◽  
Content Type ◽  
Switching Model ◽  
First Order ◽  
Order Markov Chain ◽  
Game Players ◽  
Motivation Model

PurposeThis research examined the social interactions of online game players based on the proposed motivation model in order to understand the transitions of motivation of online game. The authors also separated samples into four categories to compare the difference of different type of online game players.Design/methodology/approachThis study proposed a motivation model for online game player based on existence–relatedness–growth theory. The authors also analyze the transitions of motivations via first-order and second-order Markov chain switching model to obtain the journey of online to offline socialization.FindingsTeamwork–socialization players preferred to make friends in their online gaming network to socialize. Competition–socialization players were mostly students who played games to compete and socialize and may share experience in online or offline activities. Teamwork–mechanics players purely derived pleasure from gaming and were not motivated by other factors in their gaming activities. Competition–mechanics players may already have friends with other gamers in real life.Research limitations/implicationsMore samples can be added to generate more generalizable findings and the proposed motivation model can be extended by other motivations related to online gaming behavior. The authors proposed a motivation model for online to offline socialization and separated online game players into four categories: teamwork–socialization, competition–socialization, teamwork–mechanics and competition–mechanics. The category of teamwork–socialization may contribute to online to offline socialization area. The category of competition–mechanics may add value to the area of traditional offline socialization. The categories of competition–socialization and teamwork–mechanics may help extant literature understand critical stimulus for online gaming behavior.Practical implicationsThe authors’ findings can help online gaming industry understand the motivation journey of players through transition. Different types of online games may have various online game player's journey that can assist companies in improving the quality of online games. Online game companies can also offer official community to players for further interaction and experience exchange or the platform for offline activities in the physical environment.Originality/valueThis research proposed a novel motivation model to examine online to offline socializing behavior for online game research. The motivations in model were interconnected via the support of literature. The authors also integrated motivations by Markov chain switching model to obtain the transitions of motivational status. It is also the first attempt to analyze first-order and second-order Markov chain switching model for analysis. The authors’ research examined the interconnected relationships among motivations in addition to the influential factors to online gaming behavior from previous research. The results may contribute to extend the understanding of online to offline socialization in online gaming literature.

International Real Estate Review

2016 ◽  
Vol 19 (3) ◽  
pp. 265-296
Author(s):  
Richard D. Evans ◽  
◽  
Glenn R. Mueller ◽  
Keyword(s):  
Markov Chain ◽  
Real Estate ◽  
Cash Flow ◽  
Discounted Cash Flow ◽  
First Order ◽  
Order Markov Chain ◽  
Office Markets ◽  
Speed Up ◽  
Staying Time ◽  
Over Time

Metro market real estate cycles for office, industrial, retail, apartment, and hotel properties may be specified as first order Markov chains, which allow analysts to use a well-developed application, ¡§staying time¡¨. Anticipations for time spent at each cycle point are consistent with the perception of analysts that these cycle changes speed up, slow down, and pause over time. We find that these five different property types in U.S. markets appear to have different first order Markov chain specifications, with different staying time characteristics. Each of the five property types have their longest mean staying time at the troughs of recessions. Moreover, industrial and office markets have much longer mean staying times in very poor trough conditions. Most of the shortest mean staying times are in hyper supply and recession phases, with the range across property types being narrow in these cycle points. Analysts and investors should be able to use this research to better estimate future occupancy and rent estimates in their discounted cash flow (DCF) models.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

Special Topics in Queueing Theory

2018 ◽  
pp. 212-254
Keyword(s):  
Queueing Theory ◽  
Finite Population ◽  
Service Process ◽  
Batch Service ◽  
Priority Level ◽  
Priority System ◽  
Priority Systems ◽  
The One ◽  
Number Of Customers

Topics covered in Chapter 7 are priority systems with preemptive or non-preemptive system, systems with N classes of customers, customers in groups: bulk arrivals, batch service, balking and reneging, and finite population. In a priority system, it is assumed that there are 1, 2, 3, …, N different classes or types of customers, where Type 1 customers are the most important while class N ones are the least important. When a server is available to serve a customer from the queue, the one with the highest priority level will go to the server to start their service process. In batch service, before starting the service process, a group or batch needs to be formed with a certain number of customers.

On Stochastic Characterization of Temporal Storm Patterns

1984 ◽  
Vol 16 (8-9) ◽  
pp. 147-153 ◽  
Author(s):  
Van-Thanh-Van Nguyen
Keyword(s):  
Markov Chain ◽  
Probability Distributions ◽  
First Order ◽  
Stochastic Characterization ◽  
Order Markov Chain ◽  
Hourly Rainfall ◽  
General Stochastic Model ◽  
Storm Rainfall ◽  
Rainfall Occurrences

The present study, a continuation of a previous work by the author, suggests a new theoretical approach to the characterization of the temporal pattern of storms. A storm is defined as a continuous run of non-zero one-hour rainfall depths. A general stochastic model is developed to determine the probability distributions of cumulative storm rainfall amounts at successive time intervals after the storm began. The previous model for characterizing storm temporal patterns was based on the assumption that hourly rainfall depths were independent and identically exponentially distributed random variables, while sequences of wet hours were modeled by a first-order stationary Markov chain. Hence, the model did only introduce dependence of wet hour occurences into the rainfall process through the first-order Markov chain. The present paper proposes a more general model that can take into account both the persistence in hourly rainfall occurrences and the dependence between successive hourly rainfall depths. Results of an illustrative example show that by accounting for the correlation structure of consecutive rainfall depths the present model gives a better fit to the observations than the previous one.

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