بررسي پايداري الگوريتم کنترل ازدحام اوليه-دوگان در حضور اغتشاش خارجي
محورهای موضوعی : مهندسی برق و کامپیوترعلی معرفيان‌پور 1 , وحيد جوهری مجد 2
1 - دانشگاه تربیت مدرس
2 - دانشگاه تربیت مدرس
کلید واژه: اغتشاش خارجيالگوريتم اوليه - دوگانپايداري ورودي - حالتشبکه‌هاي کامپيوتريکنترل ازدحام,
چکیده مقاله :
در اين مقاله به بررسي اثرات اغتشاش خارجي بر سيستم حلقه بسته مسأله کنترل ازدحام در يک شبكه با ساختار عمومي مي‌پردازيم. بررسي اثرات اغتشاش از اين جنبه حائز اهميت است که بسياري از جريان‌هاي داده در شبکه اينترنت به‌عنوان جريان‌هاي مدل‌نشده در نظر گرفته مي‌شوند. برخلاف کارهاي گذشته، در اينجا هر دو بخش فرستنده‌ها و لينک‌هاي شبکه داراي ديناميک فرض مي‌شوند. هر فرستنده نرخ ارسال خود را به‌گونه‌اي محاسبه مي‌کند که تابع هزينه خود را کمينه نمايد. شبکه با استفاده از تقريب جريان سيال و انتخاب يک مدل غير خطي براي ديناميک لينک مدل‌سازي مي‌شود. در اين تحقيق، ابتدا شرايط وجود نقطه تعادل را با در نظر گرفتن مجموعه محدوديت‌هاي حاکم بر مسأله استخراج مي‌نماييم. سپس پايداري ورودي - حالت براي سيستم حلقه بسته مسأله کنترل ازدحام به‌ازاي اغتشاش‌هاي موجود در ورودي و خروجي لينک‌هاي شبکه اثبات مي‌کنيم. به‌علاوه نشان خواهيم داد در صورتي که ماتريس مسيريابي شبکه تغييرات کند باز هم نتايج به‌دست آمده براي سيستم حلقه بسته مسأله کنترل ازدحام، برقرار خواهد بود. در انتها دستاوردهاي تئوري مقاله را با استفاده از شبيه‌سازي دو شبکه چندلينک مورد ارزيابي قرار مي‌دهيم.
In this paper, we consider the effects of exogenous disturbances on the closed-loop system of the congestion control problem in a network with general structure. This investigation is important since many of data flows in internet network are considered as unmodeled flows. In contrast to previous works, we suppose that both senders and links in the network have dynamics. Each sender updates its sending rate to minimize its own cost function. The network is modeled based on fluid flow approximation with nonlinear dynamics for the links. In this research, we first derive the conditions for the existence of the system equilibrium point taking into account the constraint sets of the problem. Then, we prove input-to-state stability (ISS) of the closed-loop system for the congestion control problem with input and output disturbances in the network links. We further show that the obtain results are valid even when the routing matrix of the network varies. Finally, we verify the theoretical results by simulation on two different multi-link networks.
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