The Analysis of the Loss Rate of Information Packet of Double Queue Single Server in Bi-directional Cable TV Network

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1 Applied Mechanics and Materials Submitted: ISSN: , Vol. 665, pp Accepted: doi: / Online: Trans Tech Publications, Switzerland The Analysis of the Loss Rate of Information Packet of Double Queue Single Server in Bi-directional Cable TV Network Hongwei Ding 1, a, Yawei Yang 2,b, Jia Guo 3,c, Yong Wang 4,d, Yingying Guo 5,e and Qianlin Liu 6,f 1 Department of Communication Engineering, Yunnan University, Kunming, China 2 Yunnan University, 2 North Cuihu Road, Kunming, China 3 Radio, film and Television Bureau of Yunnan Province, Kunming, China 4 Radio, film and Television Bureau of Yunnan Province, Kunming, China 5 Yunnan University, 2 North Cuihu Road, Kunming, China 6 Yunnan provincial military command, Kunming, China a dhw1964@163.com, b @qq.com, c guojia@163.com, d wangyong@163.com, e @qq.com, f @qq.com Keywords: loss rate analysis, the Bi-directional cable TV network, double queue single server system. Abstract. The transformation of loss rate analysis for the Bi-directional cable TV network is becoming more and more important. In this paper, the authors employ the double queue single server system to the information of Bi-directional cable TV network in the analysis of information packet. The information of Bi-directional cable network packets are calculated and analyzed theoretically and the loss rate of the information packet is also simulated by computer in this paper. Simulation results show that the theoretical analysis and simulation are consistent. And the network of Bi-directional information packet using double queue single server modeling of cable television in the transformation of loss rate analysis provides reference to the theoretical analysis and computer simulation. Introduction Current market gradually expands the cable television network [1], cable network construction is gradually expanded according to the demand of market, and cable television network also promotes Bi-directional transformation which is gradually being constructed. Telecommunications network, computer network and three cable television networks are penetrated and merged through technological innovation, which are gradually integrated into a unified information and communication networks, including voice, data, images and integrated multimedia communication services [2]. Information packet that is digitized, after the Bi-directional transformation, which is from traditional broadcast network gradual transition to a variety of business network, the implementation of these operations on the follow-up technical support puts forward higher requirements. During the network transmission, the loss ratio is the proportion of the sum of packets lost count of the entire information packet, which determines the level of quality of the service to the cable television network. The cause of information Packet loss includes errors, route changes and queue overflow. This paper mainly studies the impact of arrival rate for the information service packet, which contains the theoretical derivation of formulas and computer simulation, the theoretical formula describes the relationship among the buffer, the arrival rate and packet loss rate information, the use of double queue single server system theoretical calculation and simulation; we obtain the loss rate of information packet in the Bi-directional network television. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-12/09/16,13:08:20)

2 Applied Mechanics and Materials Vol M/M/1 System Information Packet Loss Rate Information Packet Arrival Pattern. Assuming the period of any time slot and the information packets are independent of one another, with the distribution of the probability distribution of each buffer (queue space) into the information in the packet, the information which is provided to the packet arrival process is Poisson process parameters of λ, then within the time length of t,assuming the information packet arrival process is a Poisson process with the parameter of k, k ( λt) t pk ( t) = e λ, k = 0,1, 2,,where λ > 0 is a constant representing the average packet arrival k! rate information or intensity information of Poisson packet. Service Rules. Packets which advance first are serviced first according to the rule of FIFO (First-in, First-out), the service of information packets is followed by the rules of M/M/1 system [3], as a single server queue so there is no transfer time if the number of information packets into the buffer capacity of the buffer is greater than S, and will overflow packet generation information, which produce information packet loss [4]. Finite buffer system (S information packets can be stored) information packet loss rate is defined as the ratio of the number of information packets and the total loss of the packet number of the input information. The Theoretical Formula of Calculating. In this paper, assuming that the buffer is S, with probability theory and stochastic process theory, which can be obtained by derivation M/M/1 system information packet loss rate as P loss S 1 λ e λ n = ( n= 1 ( n + S)! After calculation, the theoretical loss rate and the computer simulation results are shown as Table 1, 2, 3, 4. Table 1. M/M/1 loss rate (S=2) Table 2. M/M/1 loss rate (S=3) Table 3. M/M/1 loss rate (S=4) Table 4. M/M/1 loss rate (S=5) From the above table, we can see that, with the arrival rate increases, the loss rate of packets also increases, and it indicates that the theoretical analysis and computer simulation agree well with each other.

3 676 Materials Science and Processing, Environmental Engineering and Information Technologies Double Queue Single Server System Information Packet Loss Rate Service rules. Information packet queues are in accordance with the Poisson process which reach, assuming that the capacity of the buffer is S, in accordance with the rules of art, First-In First-Out (FIFO), the first to reach the finish queue service information packet buffer, after a transition period, the server will be transferred to the second queue, when the queue server has serviced the second information packet, after a transition period, the server will be transferred to the first queue. And so the cycle continues. If any number of information packets in a queue to reach is greater than the capacity of buffer, the buffer will overflow packet generation information, which produces the information packet to be lost. Finite buffer system (S information packets can be stored) information packet loss rate is defined as the ratio of the number of information packets and the total loss of the packet number of the input information. Assuming the buffer for the S, the service rate is 1, the server s switching time is γ, the arrival of information is serviced immediately [5]. The buffer for the basic model [6] of S is shown Fig. 1 and Fig. 2 Fig. 1 Double queue single server gated service system model. λ λ Fig. 2 The principle of double queue single server gated service system diagram. The theoretical calculation formula is as below: P loss m 1 2 λ( s+ m+ n+ S 1 S m 1 n+ S 1 2 λ( S+ 2 λ( S+ S [2 λ( S + ] e n(2 mλ) [2 λ( S + ] n[2 λ( S + ] e = + [1 e ] ( m! ( n + S)! ( m! ( n + S)! m= 1 n= 1 m= 1 n= 1 m 1 2 λ( s+ m+ n+ S 1 S m 1 n+ S 1 2 λ( S + 2 λ( S+ S [2 λ( S + ] e n(2 mλ) [2 λ( S + ] n[2 λ( S + ] e = + [1 e ] ( m! ( n + S)! ( m! ( n + S)! m= 1 n= 1 m= 1 n= 1 The theoretical calculation and computer simulation results are in Table 5, 6, 7, 8 as below: Table 5. Double queue single server system with gated service(s=2) (2)

4 Applied Mechanics and Materials Vol Table 6. Double queue single server system with gated service (S=3) Table 7. Double queue single server system with gated service (S=4) Table 8. Double queue single server system with gated service (S=5) From the above table, we can conclude that the arrival rate increases, the loss rate also increases, and the theoretical analysis and computer simulation are consistent. Conclusions This paper mainly aims at the information packet arrival rate of service quality were studied, using double-queue single-server system with gated service and simulate the information Bi-directional cable TV network in packet loss rate, We can obtain the following conclusion: 1. We have obtained the analytic expression rate of missing information packet, the simulation results show that the consistency of the theoretical analysis and computer simulation has been verified by the correctness of data. 2. With the arrival rate increasing, the rate to the loss of information packet also increases. 3. With buffer size increasing, the rate to the loss of information packet also reduces. 4. Comparing with the M/M/1 communication system, dual queue packet loss rate which is closer to the actual system is significantly higher than that of M/M/1 communication system, which has certain practical significance analysis of double queue, laying the foundation for the analysis of multiple queues the next step. Corresponding author Hongwei Ding (1964-), male, Professor of Yunnan University, PhD Degree. Mainly engaged in the research of random multiple access communication system, polling system, network communication engineering. Acknowledgement This work was supported by the National Natural Science Foundation of China ( ); Natural Science Foundation of Yunnan Province (2010CD023); Graduate Scientific Research Fund of Yunnan University (ynuy201047) financial support of Yunnan University(No.XT412004). This work was also supported by radio and Television Bureau of Yunnan province innovation platform project.

5 678 Materials Science and Processing, Environmental Engineering and Information Technologies References [1] Yuming Yuan, in Qiaomeng, solution Guixing. Practical application of two way CATV coaxial cable network frequency coverage. China cable TV, (2013) [2] Li Yan, Zhao Dongfeng, Ding Hongwei, et al. Polling multiple access threshold service strategy of [J], Journal of China Institute of communications, 2005,26 (3): [3] Zhao Dongfeng, Li Bimei, Zheng Sumin. The polling system with limited service queuing system [J]. Journal of electronics, 1997, 19 (: [4] Zhang Feng, Wang Jinting. Analysis of equilibrium under complete information can repair M/M/1 queuing system. Journal of Beijing Jiaotong University, (2012) [5] Zhang Zhiyong, Yang Zuying, ET al.matlab tutorial, Peking University Aerospace Press. [6] Yang Jian, Liang Hong. The principle and practice of random signal processing, Science Press.