ارتقاء کیفیت سیستم‌های صف‌بندی M/M/m/K با استفاده از بهینه‌سازی تابع هزینه سیستم

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه آمار، دانشگاه پیام نور، تهران،ایران

چکیده
در این مقاله سیستم صف‌بندی با ظرفیت متناهی M∕M∕m∕K به ازاء m≥2 در نظر گرفته شده که در آن K ظرفیت سامانه و m تعداد خدمت دهنده‌ها است. ابتدا تابعی به نام تابع هزینه سیستم بر حسب متوسط تعداد متقاضیان در صف و سیستم و تعداد خدمت‌دهنده‌ها پیشنهاد می‌شود. سپس هدف یافتن m ای است به نام m_Opt که به ازای آن تابع هزینه مینیمم شود. در این مقاله سیستم M⁄M/m_Opt/K سیستم بهینه نامیده می‌شود. در انتها با استفاده از یک مثال عددی به ازای Kهای مختلف، سیستم‌های بهینه تعیین شده و متوسط تعداد متقاضیان در صف و سیستم، متوسط مدت زمان انتظار در صف و سیستم متقاضیان و معیاری به نام متوسط درجه رضایت متقاضی در این نوع سیستم‌ها به دست آورده می‌شود.

کلیدواژه‌ها


عنوان مقاله English

Improving the Quality of M/M/m/K Queueing Systems Using System Cost Function Optimization

نویسندگان English

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

In this article, a queuing system with finite capacity, referred to as M/M/m/K, is analyzed for m ≥ 2, where K represents the system's capacity and m indicates the number of servers. Initially, a function known as the system cost function is introduced. This function is based on the number of customers present in the queue and the number of servers available. The main objective is to identify the optimal number of servers, termed mOpt, that minimizes the system cost function. This optimal configuration, denoted as M/M/mOpt/K, is termed the optimal system. To illustrate the concept, a numerical example is provided, showcasing various values of K to determine the optimal systems. The analysis covers key performance metrics such as the average number of customers in the queue and the entire system, the average waiting time of the customers both in the queue and the system, and a metric referred to as the average degree of customer satisfaction within these queuing systems. Through this comprehensive approach, the study aims to provide valuable insights into optimizing queuing systems for better efficiency and customer satisfaction.

کلیدواژه‌ها English

The M/M/m/K queuing system
Optimal system
Cost function
Optimal number of servers
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