برآورد جدید E2-بیز پارامتر بهره‌دهی سیستم صف‌بندی چند باجه‌ای با ظرفیت نامتناهی

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه آمار، دانشگاه پیام نور، تهران، ایران.

چکیده
هدف: این پژوهش با هدف توسعه‌ یک رویکرد جدید برآورد بیزی با عنوان روش E2-بیز برای برآورد پارامتر شدت ترافیک در سیستم صف‌بندی چندباجه‌ای /M/M/c انجام شده است. با توجه به اهمیت برآورد دقیق پارامتر بهره‌دهی در بهینه‌سازی سیستم‌های خدماتی، این تحقیق به نیاز موجود برای استنتاج‌های قابل اعتمادتر در شرایط عدم‌قطعیت می‌پردازد.
روش‌شناسی پژوهش: مدل صف‌بندی M/M/c/∞ که شامل c باجه خدمت‌دهنده است، در‌نظر گرفته شد. فواصل زمانی بین ورود مشتریان دارای توزیع نمایی با پارامتر λ و فواصل زمانی خدمت دارای توزیع نمایی با پارامتر μ است. پارامتر شدت ترافیک با استفاده از روش‌های بیز، E-بیز و روش پیشنهادی جدید E2-بیز تحت تابع زیان آنتروپی عمومی برآورد شد. عملکرد برآوردگر پیشنهادی با استفاده از شبیه‌سازی مونت‌کارلو و یک مجموعه‌داده واقعی ارزیابی گردید.
یافتهها: نتایج شبیه‌سازی و تحلیل تجربی نشان داد که برآوردگر پیشنهادی E2-بیز از نظر کارایی و دقت نسبت به برآوردگرهای بیز و E-بیز عملکرد بهتری دارد. برآوردگری که میانگین مدت‌زمان انتظار مشتریان در صف را حداقل می‌کند، به‌عنوان برآوردگر بهینه انتخاب شد.
اصالت/ارزش‌افزوده علمی: این پژوهش یک رویکرد نوین برآورد E2-بیز را معرفی می‌کند که دقت برآورد پارامترها را در مدل‌های صف‌بندی تحت شرایط عدم‌قطعیت بهبود می‌بخشد. به‌کارگیری تابع زیان آنتروپی عمومی چارچوبی انعطاف‌پذیر و مقاوم فراهم می‌کند و گامی موثر در پیشبرد استنتاج بیزی در سیستم‌های تصادفی به‌شمار می‌آید.

کلیدواژه‌ها

موضوعات

عنوان مقاله English

An improved E2-Bayesian estimator for the efficiency parameter of an infinite-capacity multi-server queueing system

نویسندگان English

Shahram Yaghoobzadeh Shahrastani
Iman Makhdoom
Department of Statistics, Payame Noor University, Tehran, Iran.
چکیده English

Purpose: The study aims to develop a new Bayesian estimation approach, termed the E2-Bayesian method, for estimating the traffic intensity parameter in the multi-server M/M/c/∞ queueing system. Given the crucial role of accurate efficiency estimation in optimizing service systems, this research addresses the need for more reliable inference under uncertainty.
Methodology: The M/M/c/∞ queueing model, characterized by servers, exponential interarrival times with rate parameter λ, and exponential service times with rate parameter μ, is considered. The traffic intensity parameter is estimated using Bayesian, E-Bayesian, and the newly proposed E2-Bayesian methods under the general entropy loss function. The performance of the proposed estimator is assessed through Monte Carlo simulation and validated using a real dataset.
Findings: Simulation results and empirical analysis demonstrate that the proposed E2-Bayesian estimator outperforms the traditional Bayesian and E-Bayesian estimators in terms of efficiency and accuracy. The estimator that minimizes the mean waiting time of customers in the queue is identified as the optimal choice.
Originality/Value: This research introduces a novel E2-Bayesian estimation approach that enhances the precision of parameter estimation in queueing models under uncertainty. The integration of the general entropy loss function provides a flexible and robust framework, contributing to the advancement of Bayesian inference in stochastic systems.

کلیدواژه‌ها English

E2-Bayesian estimation, General entropy loss function, M/M/c/∞
queueing model, Mean waiting time
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