Design of delay compensation algorithm in remote auction network for digital art works

Abstract

Aiming at the problem of delay and packet loss in current remote network, a delay compensation algorithm for high-speed network is studied and applied to the remote auction of digital art works. High-speed network delay mainly includes: transmission processing delay, waiting delay, transmission delay, and reception processing delay. The delay model of high-speed network is designed by using a time division multiple access protocol. Based on the high-speed network delay model, the Kalman filter is used to design the high-speed network delay control algorithm to maintain the high-speed network delay. At the same time, the round-trip delay compensation algorithm based on link delay is used to compensate the high-speed network delay. The experimental results show that the proposed method compensates the delay of more than 235 ms, and the packet loss rate of high-speed network is only 0.59%, and the throughput reaches 241 Mbit/s, which validates the algorithm can effectively compensate the delay of high-speed network and reduce the packet loss rate of high-speed network.

Keywords

Digital art works Remote auction High speed network delay Compensation algorithm Link delay Kalman filtering

1. Introduction

There are many information sources in the high-speed network, and it needs to occupy the multi-channel data time-sharing transmission while the carrying capacity and communication bandwidth of the network are limited, resulting in information collision, retransmission, and other phenomena, so there is a high delay in the transmission process of information [3,6,9]. The delay of high-speed network greatly reduces the enforceability of communication network transmission scheme [11], and even leads to the instability of communication network. Even if the communication network remains stable, the amount of stable area is significantly reduced. Therefore, the delay problem of high-speed network has gradually attracted the attention of relevant scholars [4], and the delay compensation method of high-speed network has been deeply studied.

Shi et al. studied a new fast flooding method with real-time delay compensation for time synchronization in wireless sensor networks [12], which compensates for the delay of wireless sensor networks. The flooding delay of reference time information is significantly reduced by using the fast flooding protocol, and the joint clock skew offset maximum likelihood estimation (MLE) is designed in order to obtain accurate clock parameter estimation and real-time packet delay estimation, and achieve efficient delay compensation.; however, this method has the problem of high packet loss rate after compensation. The experimental studies show that this method can improve the delay problem of wireless sensor networks. Tian et al. studied time synchronization based on delay compensation under random delay: algorithm and experiments [16]. This method is aimed at wireless sensor networks with random bounded communication delays. It is analyzed and clarified that under the framework of a time synchronization algorithm based on consistency. Despite the drift estimation converging at a rate higher than the sampling rate, drift estimation may still diverge when there is an uncertain delay, in networks with at least two root nodes. Finally, the delay compensation mechanism is introduced in the offset estimation algorithm, and the first-order difference of offset estimation is used to adjust the delay compensation adaptively, and the upper bound of adjustment gain is given to ensure the boundedness of offset estimation, so as to realize the delay compensation of high-speed network. However, the application scope of this method is small, and it is not suitable for the diversity of high-speed network delay compensation.

Aiming at its existing problems, this paper studies the high-speed network delay compensation algorithm and applies it in remote auction based on the above three communication network delay compensation methods. This method analyzes the types of high-speed network delay in detail. Based on this, the network speech model is constructed through time division multiple access (TDMA) protocol, and the compensation method is designed in combination with the round-trip delay compensation algorithm of link delay [23] in order to effectively compensate the delay of high-speed network and improve the performance of high-speed network.

2. Analysis of high-speed network delay

2.1. Analysis of high speed network delay

The premise of solving the impact of high-speed network delay is to understand the mechanism of network delay. The delay changes with the load of high-speed network, which is time-varying and uncertain. The existence of delay reduces the network communication performance [20]. There may be many different properties of network delay (constant, bounded, random time-varying, etc.) although the analysis and modeling technology of network delay has made great progress in recent years [1,10,13], which makes the existing methods generally unable to be directly applied. And the process of information transmission is essentially the process of a device (node) on the communication network in the high-speed network, in which the task generates and sends information [17]. The data is encapsulated by various layers of protocols, parsed into packets, and reaches another device through the network channel. The delay in high-speed network can be divided into four components according to the different characteristics of the network delay generation process: transmission processing delay $T_{send}$ , waiting delay $T_{wait}$ , transmission delay $T_{ts}$ and reception processing delay $T_{rev}$ . The calculation expression of network delay is: $\begin{matrix} (1) & T_{delay} = T_{send} + T_{wait} + T_{ts} + T_{rev} \end{matrix}$

In Eq. (1), $T_{send}$ and $T_{wait}$ represent generated on the communication source node, $T_{rev}$ represents generated on the communication target node, and $T_{ts}$ represents the sum of the information transmission time and the channel propagation time. The specific analysis is as follows:

Transmission and processing delay $T_{send}$ : it includes the time taken by the communication source node to generate the application layer information packet and the time required to convert it into a suitable communication network transmission format. The transmission and processing delay mainly depends on the performance of the software and hardware of the communication source node equipment, which is predictable;

Waiting delay $T_{wait}$ : the time that data frames in the data link layer wait for the medium access control (MAC) protocol to send when sending the cache, including the queuing time in the cache queue and the time that the competitive channel waits for the channel to be idle. The waiting delay is determined by the amount of data to be sent in the source node and the traffic of the communication network at the moment. The important factors that affect the waiting delay $T_{wait}$ are MAC layer protocol, information connection mode and network load;

Transmission delay $T_{ts}$ : it includes the transmission time of the physical layer signal of the communication network sent to the channel and the transmission time of the signal on the physical channel. Transmission delay is the most deterministic parameter in the control network, because it only depends on the communication network bandwidth and the distance between two communication nodes. The expression of transmission delay is as follows: $\begin{matrix} (2) & T_{ts} = N \times T_{bit} + N \times T_{s} \end{matrix}$

In Eq. (2), N represents the number of bits of the data frame sent by the communication network, $T_{bit}$ represents the time required to send one bit, and $T_{s}$ represents the propagation time of the signal between any two nodes of the communication network. Since the propagation speed of the signal in the communication medium is $2 \times 10^{8} m / s$ , the propagation time in the short-range communication network can be ignored.

Receiving and processing delay $T_{rev}$ : the receiving and processing delay is the time when the data frame is parsed and restored to the application layer information and passed to the task. The receiving and processing delay is related to the software and hardware performance of the target node equipment. Because the other three kinds of delay depend on the software and hardware performance of the equipment or can be ignored, when the communication network parameters are fixed, it is predictable, and the waiting delay $T_{wait}$ increases with the increase of the number of communication network nodes and the amount of data. Even in the normal communication state, the traffic of the communication network is basically stable. The waiting delay will vary greatly with the different media access control mechanisms for the communication network with different protocols. When the traffic of communication network fluctuates, this difference will be greater. Therefore, the uncertainty of high-speed network delay mainly comes from the waiting delay of the MAC layer of the communication network.

2.2. High speed network delay model design

A high-speed network delay model is established based on the analysis of high-speed network delay [5,14,19]. Time-division multiple access (TDMA) protocol [15] is widely used in high-speed networks as an effective multiple access method. A TDMA protocol has N transmission units, and the transmission time of the message is divided into continuous time frames, and each time frame is composed of continuous time slots. Let τ be the size of time slots, and M be the number of time slots per frame. When the communication units of high-speed network are allocated time slot transmission messages in a certain time frame, a message will be formed every several time slots. If the message transmitted in the communication unit of the high-speed network is the number of time slots $T_{F} = M_{τ}$ , and it transmits a data packet every M time slots. $N (t)$ represents the message queue length in the high-speed network communication unit at t time, and its probability distribution can be expressed as: $\begin{matrix} (3) & P_{n} = P {N (t) = n} \end{matrix}$

The expression of probability generating function is as follows: $\begin{matrix} (4) & P (z) = \sum_{n = 0}^{\infty} P_{n} z^{n} \end{matrix}$

When the message reaches the communication network, the service time follows the random distribution principle, where n represents the communication node, $P_{n}$ represents the node set of the optimal transmission link, and z represents the node information in high-speed network communication. In order to achieve the equilibrium of energy allocation for the nodes, the probability generation function must be transformed by the second moment.

Assuming tht the communication bits of high-speed networks are distriubted independently, the message transmission process is abstracted as a queuing system. Accordng to the message first-come-first-served rule, the second moment transformation is carried out. Let $P_{0}$ represents the nitial node of the optimal transmission link and λ represents the transmission rate. The second moment transformation expression of probability generation function $P (z)$ is: $\begin{matrix} (5) & P (z) = \frac{P_{0} [z {\hat{B}}^{*} (λ - z) - B^{*} (λ - z)]}{z - B^{*} (λ - z)} \end{matrix}$

In Eq. (5), $B^{*} (s)$ and ${\hat{B}}^{*} (s)$ represent Laplace–Stilches transformations in which messages obey time distribution; $P (z)$ represents the probability generating function with the n-th messages in the communication unit; $P_{0}$ represents obtained when $z = 1$ . From Eq. (5), the expected message length $\bar{N}$ is: $\begin{matrix} (6) & \bar{N} = \frac{λ^{2} {\hat{b}}_{1}}{1 - λ (b_{1} - {\hat{b}}_{1})} + \frac{λ^{2} ({\hat{b}}_{2} - b_{2})}{3 [1 - λ (b_{1} - {\hat{b}}_{1})]} \end{matrix}$

According to $\bar{N} = λ t_{d}$ [22], the transmission delay model of the message is: $\begin{matrix} (7) & T_{ts} = \frac{F_{n 1} T_{F} - T_{F}}{2} + \frac{T_{F}}{(1 - M)} + \frac{λ F_{n 2} T_{F}^{2}}{3 (1 - λ F_{n 1} T_{F})} \end{matrix}$

Eq. (7) gives the message transmission delay when the communication unit of the high-speed network allocates only one time slot in each time frame. This conclusion is generalized, that is, the communication unit allocates multiple time slots in each time frame, and the allocated time slot positions are evenly distributed in the time frame. Suppose that the number of time slots allocated by the communication unit in each time frame is $n_{i}$ , and replace $T_{F}$ with $\frac{T_{F}}{n_{i}}$ in Eq. (7), we can get: $\begin{matrix} (8) & T_{ts} = \frac{F_{n 1} T_{F}}{n_{i} - 2 n_{i}} + λ \frac{T_{F}}{M n_{i}} + \frac{λ F_{n 2} {(\frac{T_{F}^{2}}{n_{i}})}^{2}}{2 (1 - \frac{λ F_{n 1} T_{F}}{n_{i}})} \end{matrix}$

According to the TDMA protocol, let each message consists of only one packet, that is, $F_{n 1} = F_{n 2} = 1$ . Then, according to Eq. (8), the changes of message arrival rate λ, service rate μ and transmission delay time can be obtained. It can be seen that the transmission delay time of high-speed network is related to the service rate μ and arrival rate λ of messages. When λ is constant, the delay time of high-speed network decreases with the increase of μ; When μ is constant, the delay time of high-speed network increases with the increase of λ; When $λ = μ$ , the transmission delay time of high-speed network increases sharply.

2.3. High speed network delay control algorithm

A high-speed network delay control algorithm based on Kalman filter is designed for the established high-speed network delay model, the route detection protocol of high-speed network transmission process is designed by the shortest path optimization method, and the fractional interval equilibrium control model of high-speed network output is constructed. The adaptive allocation function of the geometric center position of each region of high-speed network is obtained as follows: $\begin{matrix} (9) & | s (f) | = A \sqrt{\frac{1}{2 k} {{[c (t_{1}) + c (t_{2})]}^{2} + {[s (t_{1}) + s (t_{2})]}^{2}}} \end{matrix}$

In Eq. (9), A represents the amplitude of information collected by high-speed network and compressed sensing, $k = B / T$ represents the frequency modulation slope, and B represents the equilibrium configuration coefficient after several rounds of data collection; $c (t)$ and $s (t)$ respectively represent different locations in the high-speed network. Combined with the energy balance method of remaining nodes, the optimal sampling model of high-speed network transmission is established, and the optimal configuration function is $\hat{f} (x, y) = β F (x, y) + (1 - β) m_{l}$ , where $F (x, y)$ represents the residual mean square error. At the characteristic point $(x, y)$ of data transmission of high-speed network, the energy load threshold of nodes around the link is $β = max [\frac{δ_{l}^{2} - δ_{η}^{2}}{δ_{l}^{2}}, 0]$ , the energy coefficient of the $j = 0, 1, \dots, M$ symbol sequence is $E_{j} = \sum_{k} | T_{ts} |^{2}$ , and the transmission delay of high-speed network is $T_{ts} = [x (t), φ_{j, k} (t)]$ . Using the discrete scheduling method, the Kalman filter coefficient of low delay output of high-speed network data is obtained as: $\begin{matrix} (10) & E = {‖ x (t) ‖}^{2} = \sum_{j} \sum_{k} | T_{ts} |^{2} = \sum_{j} E_{j} \end{matrix}$

Using the node self-detection method, the characteristic distribution coefficient of high-speed network modulation and demodulation can be expressed as: $\begin{matrix} (11) & g (t) = \frac{1}{\sqrt{a_{0}}} f \frac{t - τ_{0}}{a_{0}}, \end{matrix}$ where $a_{0}$ is the number of subcarriers, f is the RF gain, and $τ_{0}$ is the initial time slot.

To sum up, the normalized root mean square error modulation method of neighbor node set is adopted to balance the output capacity, and establish the delay error compensation model of high-speed network. The output delay error is $P_{j} = E_{j} / E$ , and the comparison function between nodes is: $\begin{matrix} (12) & y (n) = x (n) * h (n) + \hat{x} (n) n (n) * W (n) \end{matrix}$

In Eq. (12), $\hat{x} (n)$ represents the node state set of high-speed network, $h (n)$ is the preset channel fading characteristic quantity, $n (n)$ represents the interference component of high-speed network data transmission process, and $W (n)$ represents the multipath response characteristic quantity.

The optimal function of low delay control of high-speed network obtained by using multipath expansion method is: $\begin{matrix} (13) & \{\begin{matrix} H_{0} : x (t) * h_{w} (t) = w (t) \\ H_{1} : \sqrt{E} s (t) * h_{w} (t) + w (t) \end{matrix} 0 ⩽ t ⩽ T \end{matrix}$

Using the above process, the low delay control of high-speed network data transmission process is realized, and the channel allocation and error compensation of high-speed network are carried out according to the delay control results, so as to improve the anti-interference ability of high-speed network data transmission.

2.4. Round trip delay compensation algorithm based on link delay

The round-trip delay compensation algorithm [23] based on link delay is used to compensate the high-speed network delay based on the high-speed network delay control [2,7,8]. There are often great differences between high-speed network communication paths, which cannot ensure that the round trip time (RTT) of each path is equal. Learn from the biogeography-based optimizatio (BBO) routing idea [18]. When balancing the delay congestion of high-speed network, balance the load on each subflow according to the bandwidth occupation ratio of each subflow. The implementation process is that when a confirmation character is received on the subflow, the congestion window $W_{r} : a / W_{total}$ is increased, when packet loss is detected on the subflow, reduce the congestion window $W_{r} : max [β \times W_{r}, W_{r} / 2]$ .

The round-trip delay compensation algorithm based on link delay considers the influence of different link delays of each subflow on the growth of subflow window, and the influence of round-trip delay $R_{r}$ of subflow r, which is reflected by the aggression factor a. The algorithm takes the bandwidth occupation ratio β of each subflow as the flow control parameter to balance congestion. Here, $W_{r}$ represents the congestion control window on the r-th sub stream of the high-speed network, $R_{r}$ represents the loop time value on the r-th sub stream, $W_{total}$ represents the sum of the congestion windows of the high-speed network, and α represents the aggression factor. It is a parameter to ensure that the multi-path transmission control protocol sub stream of the high-speed network can compete with the transmission control protocol stream fairly and share the bottleneck link. The ratio of the bandwidth on the sub stream r to the total bandwidth is $i_{r}$ (referred to as the occupancy ratio), β is the flow balance parameter of each subflow, and the calculation formula is as follows: $\begin{matrix} (14) & β = (\sum_{i} \frac{W_{i}}{R_{i}}) / (w \times \frac{W_{r}}{R_{r}}) \end{matrix}$

The sleep of high-speed network interface will lead to the loss of transmission data. It is assumed that all paths of high-speed network have the same packet loss rate. Each window is increased by the confirmation character, and the packet loss is reduced. There must be a balance between the increase and decrease of the equation. Therefore, the set α must meet the equation, that is, “receipt Acknowledgement (ACK) rate” × “Average increment per confirmed character” = “packet loss rate” × “average reduction per packet loss”. The equation is as follows: $\begin{matrix} (15) & (\frac{W_{r}}{R} (1 - \frac{a}{β \times W_{r} \times W_{total}})) \frac{α}{W_{total}} = (\frac{W_{r}}{R} \frac{a}{β \times W_{r} \times W_{total}}) \times β \times W_{r} \end{matrix}$

According to the first goal of multipath transmission control protocol – congestion control protocol: the throughput of a multipath transmission control protocol flow is not lower than that of any transmission control protocol under the optimal single path, we can get: $\begin{matrix} (16) & \sum_{r} \frac{W_{r}}{R_{r}} ⩾ max_{r} \frac{W_{r}^{TCP}}{R_{r}} \end{matrix}$

The second goal: the capacity of a multi-path flow to preempt any shared resources from different paths cannot be more than that obtained when a single data flow is transmitted in a single path, that is: $\begin{matrix} (17) & \sum_{r} \frac{W_{r}}{R_{r}} ⩽ max_{r} \frac{W_{r}^{TCP}}{R_{r}} \end{matrix}$

In order to meet the first and second objectives of congestion control of high-speed network multipath transmission control protocol, a joint expression is established as follows: $\begin{matrix} (18) & \sum_{r} \frac{W_{r}}{R_{r}} = max_{r} \frac{W_{r}^{TCP}}{R_{r}} \end{matrix}$

In Eq. (18), $W_{r}^{TCP}$ represents the size of the congestion window when the single path transmission control protocol is running on path r. According to the limit window size equation of the standard transmission control protocol, the formula is as follows: $\begin{matrix} (19) & W_{r}^{TCP} = \sqrt{2 / p_{r}} \end{matrix}$

Integrating the above analysis process, we can deduce the expression of α as follows: $\begin{matrix} (20) & α = 2 \times β \times W_{total} \times {(\frac{{max}_{r} \sqrt{W_{r}} / R_{r}}{\sum_{r} W_{r} / R_{r}})}^{2} \end{matrix}$

It can be seen from the expression that in the round trip delay compensation algorithm of link delay [21], the aggression factor α is determined by the round trip delay, $W_{total}$ and $W_{r}$ . Through the above process, the compensation of high-speed network delay is realized.

3. Results

This method is applied to the high-speed network of a digital art remote network auction in order to verify the performance of the studied high-speed network delay compensation algorithm in high-speed network. The bandwidth of the high-speed network is 26.8 kbps, the working frequency band is 1024 mhz, and the packet length is 85 bytes. The specific experimental parameters are shown in Table 1.

Statistics of communication delays changes in high-speed networks. If the delay is more than 200 ms, it indicates a packet loss in the online remote auction of digital artwork. Compare the changes of communication delay in high-speed networks before and after applying the developed algorithm, the results of delay distribution in certain high-speed networks are shown in Fig. 1. By analyzing the experimental results in Fig. 1, we can see that the delay distribution of high-speed network is periodic, but it is not a fixed period. The delay of the network is fluctuating, but it can be stable in a fixed range in a short time. Before using this algorithm to compensate the network delay, there is obvious packet loss in the auction network, and the delay is high. After using this algorithm to compensate the delay, there is no packet loss in the network, and the communication delay has been significantly reduced, which verifies the effectiveness of this algorithm.

Table 1
Experimental parameter settings

Serial number Name Parameter

1 High speed network bandwidth 26.8 Kbps

2 Working frequency band 1024 MHz

3 Packet length 85bytes

4 Sampling period 0.08 s

5 Data transfer protocol TCP/IP

6 Data exchange mode Ethernet

7 PC Ethernet

8 High precision performance counter SYN5636

Serial number	Name	Parameter
1	High speed network bandwidth	26.8 Kbps
2	Working frequency band	1024 MHz
3	Packet length	85bytes
4	Sampling period	0.08 s
5	Data transfer protocol	TCP/IP
6	Data exchange mode	Ethernet
7	PC	Ethernet
8	High precision performance counter	SYN5636

Fig. 1.

High-speed network latency distribution in remote auctions of digital artworks.

When the high-speed network is running, the throughput of the communication network changes, and the throughput change results of the algorithm in this paper are compared with the algorithms [12,16]. The results are shown in Fig. 2.

Fig. 2.

Variation of high-speed network throughput in remote auctions of digital artworks.

The throughput has been significantly improved after the algorithm in this paper is used to compensate the high-speed network delay according to the experimental results in Fig. 2. The maximum throughput of this method is 241 Mbit/s, and the maximum throughput of the literature method is only 212 Mbit/s and 139 Mbit/s, which is 29 Mbit/s and 102 Mbit/s higher than the literature method, the experimental results in Fig. 2 show that using this algorithm to compensate network delay can effectively compensate network delay and improve network throughput.

When the algorithm in this paper is used to compensate the network delay, the packet loss rate of the communication network, and the algorithm in this paper is compared with the algorithm [12,16]. The comparison results are shown in Fig. 3.

Fig. 3.

High-speed network packet loss rate in remote auction of digital artworks.

From the experimental results in Fig. 3, it can be seen that the packet loss rate of high-speed network using the algorithm in this paper to compensate the delay of high-speed network is significantly lower than that of the algorithms [12,16]. The packet loss rate is the direct embodiment of the network communication delay state. According to data analysis, the highest packet loss rate of this method is only 0.59%, while the lowest packet loss rate of literature [12] method and literature [16] method reaches 2.58% and 1.21%. Compared with the three methods, this method reduces 1.99% and 0.62%, therefore, using this algorithm to compensate the high-speed network delay, the packet loss rate of the high-speed network is significantly reduced, indicating that the delay of the high-speed network has been significantly improved, which verifies that this algorithm is effective for the high-speed network delay compensation.

The compensation of network delay when different digital artworks are auctioned on the network is counted after the algorithm in this paper is used to compensate the high-speed network delay. The statistical results are shown in Table 2.

Table 2

Compensation results of high-speed network delay in remote auction of digital artworks

Digital Art Auction Serial Number	Original network delay/ms	Delay in the proposed method size/ms	Network delay after compensation/ms
1	584	385	199
2	641	294	347
3	584	285	299
4	751	504	247
5	594	312	282
6	384	284	100
7	564	235	329
8	1052	754	298
9	845	535	310
10	945	615	330

It can be seen that the algorithm in this paper can effectively compensate the delay of high-speed network from the experimental results in Table 2, the method compensates the delay of more than 235 ms, and the maximum value reaches 754 ms. After compensation by the algorithm in this paper, the delay of high-speed network is significantly reduced. It improves the defects of slow communication speed and affects the practical application in the high-speed network, improves the applicability of the high-speed network, and helps both sides of the auction transaction successfully complete the remote auction of digital art works.

4. Conclusion

The high-speed network has a long delay, which leads to serious packet loss of network data. In order to improve the throughput of the high-speed network, this paper designs a high-speed network delay compensation algorithm by using the Eq. (9) to Eq. (20) in order to improve the packet loss caused by network delay in high-speed network, and applies this algorithm to the practical application of network auction. It also showed that the developed algorithm can effectively improve the communication delay of high-speed network and improve the real-time performance of auction. Experimental results show that the algorithm has better performance in compensating for the delay of high-speed networks and reduces the delay overhead of high-speed networks. The proposed method can be used in future remote sensing research.

Footnotes

Acknowledgements

This paper was funded by the Jiangxi Province Literature and Art Federation Project (Jiangxi Federation of Literature and Art) under no. [2017]024.

Conflict of interest

None to report.

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