臺灣博碩士論文加值系統

對於一先到先服務的單一等級顧客，Naor [1969] 證明了在群體最佳化的條件下所獲得的排隊長度，會小於等於在顧客自身最佳化的條件下所獲得的最佳排隊長度。在此篇論文中，我們延伸Naor [1969] 的研究範圍推廣至多等級的資源共享服務系統。
我們首先推導單一等級顧客的自身最佳化和群體最佳化排隊模型的門檻限制，並從這些門檻發現令人驚異且又不一致的不等式。接著，我們考慮兩種不同等級顧客的模型，研究兩種對群體最佳化的策略，並且和自身最佳化的結果比較。最後，我們指出藉由徵收服務費，系統管理者可以控制進入系統的顧客流量在一最適合系統的情況，使之到達群體最佳化。

For the single-class queue under first-come-first-serve, Naor [1969] showed that the queue length
under overall optimization is less than or equal to that under self
optimization. In this study, we extend the scope of Naor's research to the
system with multiple classes of service under processor-sharing.
We start with deriving the thresholds of queue length under self and overall
optimization in single-class case. We show there are surprising and
inconsistent inequalities between these thresholds.
Next, we consider multiple-class case. We study two policies for
overall optimization and compare them with self optimization. Finally, we show that
by levying tolls, the system administrator can control the flow of the
entering customers in the most suitable situation for the system to reach
the overall optimization.

1 Introduction 3
2 Model Characteristics 5
2.1 Description of the Model of the Internet 5
2.2 Some Properties of the Model 6
3 Single-class Queue 6
3.1 Self Optimization 6
3.2 Overall Optimization 10
3.3 Numerical Results 12
3.4 Entrance Fee Imposition 14
4 Multiple-class Queues 16
4.1 Self Optimization 17
4.2 Overall Optimization 22
4.2.1 Policy 1 22
4.2.2 Policy 2 24
4.2.3 Numericak Results 25
5 Conclusions 29

1.A. Gupta, D. O. Stahl, A. B. Whinston, 'A Stochastic Equilibrium Model of Internet Pricing,' Journal of Economic Dynamics and Control, Vol. 21 , 697-722, 1997.
2.B. Sengupta, D. L. Jagerman, 'A Conditional Response Time of the M/M/1 Processor-Sharing Queue,' AT&T Technical Journal, Vol. 64, No. 2, February, 409-421, 1985.
3.Mackie-Mason, J. K., and H. R. Varian, 'Pricing the Internet' , in: B. Kahin and J. Keller, eds., Public Access to the Internet (Prentice-Hall, Englewood Cliffs, NJ), 269-314, 1995a.
4.Mackie-Mason, J. K., and H. R. Varian, 'Pricing congestible resources,'IEEE Journal of Selected Areas in Communications, 1995b.
5.Mackie-Mason, J. K., and H. R. Varian, 'Some Economics of the Internet, in Networks, Infrastructure, and the New Task for Regulation,' 107-136,1996.
6.Mackie-Mason, J. K., and H. R. Varian, 'A Smart Market for Resource Reservation in a Multiple Quality of Service Information Network,' 1997.
7.F. P. Kelly, 'Reversibility and Stochastic Networks,' Wiley series in probability and mathematical statistics, 1979.
8.P. Naor, 'The Regulation of Queue Size by Levying Tolls,'Econometrica, Vol. 37, No. 1, January, 15-24, 1969.
9.Sheldon M. Ross, 'Stochastic Processes,'John Wiley & Sons, inc. 2nd., 1983.