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Forecasting Annual International Tourist arrivals in Zambia Using Holt-Winters Exponential Smoothing

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Open Journal of Statistics 2019年第2期9卷 258-267页

作者： Stanley Jere Alick Banda Bornwell Kasense Ian Siluyele Edwin Moyo Department of Mathematics and Statistics Mulungushi University Kabwe Zambia Zambia Information and Communications Technology Authority Lusaka Zambia Department of Mathematics and Statistics Northrise University Ndola Zambia

Tourism is one of the major contributors to foreign exchange earnings to Zambia and world economy. Annual International tourist arrivals in Zambia from 1995 to 2014 are considered in this paper. In this study we evaluated the model performance of Auto-Regressive Integrated Moving Average (ARIMA) and Holt Winters exponential smoothing (HWES). The error indicators: Mean percentage error (MPE), Mean absolute error (MAE), Mean absolute scaled error (MASE), Root-mean-square error (RMSE) and Mean absolute percentage error (MAPE) showed that HWES is an appropriate model with reasonable forecast accuracy. The HWES (α = 1, β = 0.1246865) showed smallest error than those of the ARIMA (0, 1, 2) models. Hence, the HWES (α = 1, β = 0.1246865) can be used to model annual international tourist arrivals in Zambia. Further, forecasting results give a gradual increase in annual international tourist arrivals of about 42% by 2024. Accurate forecasts are key to new investors and Policymakers. The Zambian government should use such forecasts in formulating policies and making strategies that will promote the tourism industry.

关键词： Zambia International Tourist arrivals Holt-Winters Model ARIMA Forecasting

Server Workload in an M/M/1 Queue with Bulk arrivals and Special Delays

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Applied Mathematics 2012年第12期3卷 2174-2177页

作者： Percy H. Brill Myron Hlynka Department of Management Science University of Windsor Windsor Canada Department of Mathematics & Statistics University of Windsor Windsor Canada

We consider a variant of M/M/1 where customers arrive singly or in pairs. Each single and one member of each pair is called primary;the other member of each pair is called secondary. Each primary joins the queue upon arrival. Each secondary is delayed in a separate area, and joins the queue when “pushed” by the next arriving primary. Thus each secondary joins the queue followed immediately by the next primary. This arrival/delay mechanism appears to be new in queueing theory. Our goal is to obtain the steady-state probability density function (pdf) of the workload, and related quantities of interest. We utilize a typical sample path of the workload process as a physical guide, and simple level crossing theorems, to derive model equations for the steady-state pdf. A potential application is to the processing of electronic signals with error free components and components that require later confirmation before joining the queue. The confirmation is the arrival of the next signal.

关键词： M/M/1 Queue Bulk arrivals Delay before Joining Workload Integral Equations Level crossing Method

Chinese Mainland Remains Top Source of Visitor arrivals to Singapore

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China Report ASEAN 2019年第2期4卷 8-8页

The Singapore Tourism Board announced on February 13 that the Chinese mainland held onto its rank as Singapore’s top visitor arrival source market for a second year.

关键词： Visitor arrivals Singapore Chinese Mainland

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

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Applied Mathematics 2018年第2期9卷 153-170页

作者： A. Lorente M. S. Sánchez Departamento de Matemáticas y Computación Universidad de Burgos Escuela Politécnica Superior Avda. Cantabria s/n 09006 Burgos Spain Departamento de Matemáticas y Computación Universidad de Burgos Facultad de Ciencias Pza. Misael Ba&ntilde uelos s/n 09001 Burgos Spain

This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch arrivals of fixed size a, and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time.

关键词： Discrete-Time Queuing System Batch arrivals Batch Services Stationary Systems

A Two Stage Batch Arrival Queue with Reneging during Vacation and Breakdown Periods

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American Journal of Operations Research 2013年第6期3卷 570-580页

作者： Monita Baruah Kailash C. Madan Tillal Eldabi Brunel Business School Brunel University London UK College of Information Technology Ahlia University Manama Bahrain

We study a two stage queuing model where the server provides two stages of service one by one in succession. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. We concentrate on deriving the steady state solutions by using supplementary variable technique and calculate the mean queue length and mean waiting time. Further some special cases are also discussed and numerical examples are presented.

关键词： Two-Stage Service Batch arrivals Breakdowns Reneging Steady State Queue Size