Over the years, there has been an unimaginable growth in the usage of the Internet across the globe. However, the range of applications being deployed across the Internet today is far broader than it was a few years back [1]. As it can be observed, traditional applications such as bulk file transfer (e.g. E-mail), and static websites are no longer sufficient for today’s Internet requirement, hence the need for the deployment of wider spectrum of applications. Applications that rely on the real-time delivery of data, such as video conferencing tools, Internet telephony, as well as video and audio streaming (referred to as multimedia applications) are fast gaining prominence in the Internet application space [1,2]. Video streaming, a multimedia application enables simultaneous delivery and playback of the video which overcomes the problems associated with file download since users do not have to wait for the entire video to be received before viewing it [3]. There are two types of streaming applications depending on whether the video is pre-encoded and stored for later viewing, or it is captured and encoded for real-time communication [4]. These new applications (real-time multimedia streaming, video-on-demand etc.) have diverse quality of service (QoS) requirements that are significantly different from traditional best effort service. QoS means that delays, transmission rates, error rates and other characteristics can be measured, improved upon, and to some extent, guaranteed in some advance [5]. Users consider delays larger than 300 ms not suitable for interactive conversation [6]. Therefore concerted effort has to be made to keep within this range. Since the Internet is a best-effort network and does not guarantee quality of service [7], several problems have to be solved before low delay streaming, suitable for inter-active communication via the Internet can be widely deployed. These problems include: Bandwidth variation, Packet loss, Bit (Packet) errors, Packet delay variation (PDV). Though non-real time applications can still adapt to these challenges [8], they are however responsible for the poor quality delivery in real-time multimedia transmission which should ensure smooth playout rate and hence highly interactive [9,10]. Employing the Internet as a medium of transmission of real-time interactive video is a challenging task especially in a slow-speed link environment. Slow-Speed link is defined as data transmission speed of at most 4 Megabits per second (Mbps), downstream (from the Internet to the user’s computer) and 1 Mbit/s upstream (from the user’s computer to the Internet) according to the United States (US) Federal Communications Commission [11]. Any speed less than 4 Mbits/s downstream and 1Mbit/s upstream is considered slow and may not be suitable for real-time multimedia traffics transmission. Heterogeneity in Internet access and dynamic variability in network conditions have brought about the need to design network-adaptive video applications [12]. Frame rate adaptor is a traffic shaping scheme that enhances the transmission of multimedia applications across the network. It automatically regulates the video frames rates according to network congestion level [13]. Traffic shaper represents a complete system that provides high interactivity while adapting to a poor network condition [14]. This is achieved by adjusting transmission rate and controlling the quality of the received streams. Token bucket and Leaky bucket are techniques used to implement the double-buffer traffic shaper [15].

Real-time multimedia application transmission has been an active area of research. [16] studied an efficient delay distribution scheme that allocates the end-to-end delay bound into the end-station shaper and the network. They reviewed the effect of switch delay and shaping on network performance based on the empirical envelope traffic model, and analyzed the impact of shaping via computer simulations [1] offered a system design and implementation that ameliorates some of the important problems with video streaming over the Internet. He leveraged the characteristics of MPEG-4 to selectively retransmit the most important data in order to limit the propagation of errors. [5] presented an implementation of an end-to-end application for streaming stored MPEG-4 Fine-Grained Scalable (FGS) videos over the best-effort Internet. There scheme adapts the coding rate of the streaming video to the variations of the available bandwidth for the connection, while smoothing changes in image quality between consecutive video scenes. Ioan and Niculescu in [17] proposed two mathematical models of an algorithm named Leaky bucket mechanism used for the parameter usage of connection control in multimedia networks.Bajic et al., in [18] addressed the issue of robust and efficient scalable video communication by integrating an end-to-end buffer management and congestion control at the source with the frame rate playout adjustment mechanism at the receiver. Lam et al., in [19] addressed the challenge of the lack of end-to-end quality of service support in the current Internet which caused significant difficulties to ensuring playback continuity in video streaming applications by investigating a new adaptation algorithm to adjust the bit-rate of video data in response to the network bandwidth available to improve playback continuity. In [20], Dubious and Chiustudied statistical multiplexing of VBR video in ATM networks. ATM promises to provide high speed real-time multipoint to central video transmission for telemedicine applications in rural hospitals and in emergency medical services. The ramifications of this technology are clear: speed, reliability (lower loss rate and jitter), and increased capacity in video transmission for telemedicine. [3] studied the buffering schemes for the VBR video streaming in heterogeneous wireless networks. The proposed adaptive rate control algorithms provide significantly improved streaming quality compared with the non-control policy. [13] asserted that the great endto-end delays are the major factor  influencing the visual quality of real-time video across the Internet using TCP as transport layer protocol. Xiong et al. in [21] again pointed the requirement for transmitting real-time video with acceptable playing performance via TCP and presented a stochastic prediction model which can predict the sending delays of video frames.

However, these available frame rate adaptation techniques are not suited for slow speed network environment. It is therefore imperative to develop a new technique that will meet this challenge. Double buffer traffic shaper is thus presented.

A Markov process with states can be characterized by its. Matrix Q’s entry in the column of the row of the matrix is being the instantaneous transition rate. is the sum of the parameters labeling arcs connecting states and in the transition rate diagram. The diagonal elements are chosen to ensure that the sum of the elements in every row is zero, i.e.

The infinitesimal generator matrix for the transition rate diagram of the M/D/1/K queue of Figure 3 is shown in Equation (5). It is a matrix, meaning that it has 13 states. The values for the parameters

expressed in Equation (3.4) were obtained from the transitions from one state to another. Therefore,

In solving the matrix Equation, in equation 5, the parameter values were inserted. The whole equation is thereafter transposed. i.e. becomes. This enabled the right hand side to be converted to column vector of zeros rather than the initial row vector.

In other to resolve the problem of redundancy amongst the global balance equation, one of the global balance equations was replaced by the normalization condition. In the transposed matrix, this corresponds to replacing one row (last row) by a row of 1’s and also change the solution vector, which was all zeros to be a column vector with 1 in the last row, and zero everywhere else. This vector is denoted by, and the modified matrix is denoted by. It then becomes

When Equation (7) was solved, the stationary probabilities were obtained as presented in (8). The state based performance measures are those which clearly correspond to the probability that the model is in a state, or a subset of states which satisfy some condition. Therefore, utilization in the proposed model corresponds to those states in which service took place (states) on M/D/1/K Queue. i.e

The analytical utilization of M/D/1/K queue is about 23.08%.

Matlab 7.0 was used in simulating the proposed algorithm. H.263 trace data obtained from Verbose Jurassic standard data set was used as the test data. The data file is a one-hour video session, and it is composed of 25,432 frames. Frame rate arrival into the first buffer was set according to the principle of H.263 encoder. Arrival rate into the second buffer is obtained from the operation of the algorithm introduced at the server of the first queue.

The volume of frames in the buffer is obtained from the accumulation of frames as a result of delay experienced by the frames. As shown in Figure 6, the initial 400 seconds of the video session shows a steady increase in the number of video frames to around 230 frames. The quantity however steadily reduced to zero within the proceeding 500 seconds. The volume rose to 250 frames at 1600 seconds and lingered at that point for 200 seconds. It thereafter dropped to less than 40 video frames for about 25% of the simulation period. It however peaked to 370 video frames towards the last 200 seconds of the simulation of the video session.

Again when the proposed scheme was compared with the existing scheme in terms of buffer occupancy, it was observed that the existing scheme outperformed the proposed scheme in most part of the simulation duration as can be seen in Figure 7. This performance is evident in the overall quantity of frames in the buffer per unit time. Throughout the duration of the simulation, the quantity of frames in the existing scheme was constantly below 100 frames; it was highly bounded, while that of the proposed DBFR scheme hovered between 0 and 300 frames for more than 95% of the simulation duration.

For closer observation of the interesting points and disparities of the buffer fullness of the existing and proposed schemes, the simulation period was divided into six epochs.

Figure 8 compares the two schemes for the first 200 seconds, it was noticed that for during the first 160 seconds, the proposed scheme performed excellently by maintaining a buffer fullness lower than the existing scheme. Figure 9 represents the buffer fullness between 200 - 700 seconds. This shows that the buffer fullness in the proposed scheme increased steadily to about 300 frames while the existing scheme did not exceed 100 frames. The two schemes later reduced the buffer fullness during which the existing scheme crashed to as low as 3 to 10 frames for almost 50% of the time duration, the proposed scheme reduced buffer fullness to as low as 50 frames. In the third epoch shown in Figure 10, the two schemes’ performance was very close. They both maintained a fullness of about 50 frames throughout the duration (701 and 1100) seconds. Between 1101 and 2000 seconds, there was a remarkable difference in the performance of the two schemes as seen in Figure 11.