• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.2
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• pp.236-247
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• 2002

We propose a cell－multiplexing scheme for the real－time communication service in ATM network and a new service discipline guarantee end-to-end delay based on pseudo-isochronous cell switching. The proposed scheme consists of two level frame hierarchy, upper and lower frame, which is used to assign the bandwidth and to guarantee the requested delay bound, respectively. Since the Proposed algorithm employs two level frame hierarchy, it can overcome the coupling problem which is inherent to the framing strategy It can be comparatively reduce the complexity, and still guarantee the diverse delay bounds of end-to-end. Besides, it consists of two components, traffic controller and scheduller, as the imput traffic description model and regulates the input traffic specification. The function of the traffic controller is to shape real -time traffic to have the same input pattern at every switch along the path. The end-to-end delay is bounded by the scheduller which can limit the delay variation without using per-session jitter controllers, and therefore it can decrease the required buffer size. The proposed algorithm can support the QoS's of non-real time traffic as well as those of real time traffic.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.5C
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• pp.445-453
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• 2002

We propose a cell-multiplexing scheme for the real-time communication service in ATM network and a new service discipline guarantee end-to-end delay based on pseudo-isochronous cell switching. The proposed scheme consists of two level frame hierarchy, upper and lower frame, which is used to assign the bandwidth and to guarantee the requested delay bound, respectively. Since the proposed algorithm employs two level frame hierarchy, it can overcome the coupling problem which is inherent to the framing strategy. The proposed scheme consists of two components, traffic controller and scheduller, as the imput traffic description model and regulates the input traffic specification. The function of the traffic controller is to shape real-time traffic to have the same input pattern at every switch along the path. The end-to-end delay is bounded by the scheduller which can limit the delay variation without using per-session jitter controllers, and therefore it can decrease the required buffer size. The proposed algorithm can support the QoS's of non-real time traffic as well as those of real time traffic