Mercurial > forge
changeset 12390:9dd0468b50e7 octave-forge
Fixed texinfo documentation
author | mmarzolla |
---|---|
date | Sat, 08 Mar 2014 15:55:05 +0000 |
parents | 4fa782b50c19 |
children | 1d0d979e5770 |
files | main/queueing/inst/ctmcbd.m main/queueing/inst/dtmcbd.m main/queueing/inst/engset.m main/queueing/inst/erlangb.m main/queueing/inst/erlangc.m main/queueing/inst/qncmmvaap.m main/queueing/inst/qsmh1.m main/queueing/inst/qsmm1.m main/queueing/inst/qsmm1k.m main/queueing/inst/qsmminf.m main/queueing/inst/qsmmm.m main/queueing/inst/qsmmmk.m |
diffstat | 12 files changed, 32 insertions(+), 63 deletions(-) [+] |
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--- a/main/queueing/inst/ctmcbd.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/ctmcbd.m Sat Mar 08 15:55:05 2014 +0000 @@ -32,7 +32,6 @@ ## ## Matrix @math{\bf Q} is therefore defined as: ## -## @iftex ## @tex ## $$ \pmatrix{ -\lambda_1 & \lambda_1 & & & & \cr ## \mu_1 & -(\mu_1 + \lambda_2) & \lambda_2 & & \cr @@ -44,10 +43,8 @@ ## & & & & \mu_{N-1} & -\mu_{N-1} } ## $$ ## @end tex -## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and -## death rates, respectively. -## @end iftex ## @ifnottex +## ## @example ## @group ## / \ @@ -64,6 +61,9 @@ ## @end example ## @end ifnottex ## +## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and +## death rates, respectively. +## ## @seealso{dtmcbd} ## ## @end deftypefn
--- a/main/queueing/inst/dtmcbd.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/dtmcbd.m Sat Mar 08 15:55:05 2014 +0000 @@ -33,7 +33,6 @@ ## ## Matrix @math{\bf P} is therefore defined as: ## -## @iftex ## @tex ## $$ \pmatrix{ (1-\lambda_1) & \lambda_1 & & & & \cr ## \mu_1 & (1 - \mu_1 - \lambda_2) & \lambda_2 & & \cr @@ -45,9 +44,6 @@ ## & & & & \mu_{N-1} & (1-\mu_{N-1}) } ## $$ ## @end tex -## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and -## death probabilities, respectively. -## @end iftex ## @ifnottex ## @example ## @group @@ -65,6 +61,9 @@ ## @end example ## @end ifnottex ## +## @noindent where @math{\lambda_i} and @math{\mu_i} are the birth and +## death probabilities, respectively. +## ## @seealso{ctmcbd} ## ## @end deftypefn
--- a/main/queueing/inst/engset.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/engset.m Sat Mar 08 15:55:05 2014 +0000 @@ -28,18 +28,15 @@ ## request service is exponentially distributed with mean @math{1 / ## \lambda}), and offered load @math{A = \lambda / \mu}. ## -## @iftex -## +## @tex ## @math{P_b(A, m, n)} is defined for @math{n > m} as: ## -## @tex ## $$ ## P_b(A, m, n) = {{\displaystyle{A^m {n \choose m}}} \over {\displaystyle{\sum_{k=0}^m A^k {n \choose k}}}} ## $$ -## @end tex ## ## and is 0 if @math{n @leq{} m}. -## @end iftex +## @end tex ## ## @strong{INPUTS} ##
--- a/main/queueing/inst/erlangb.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/erlangb.m Sat Mar 08 15:55:05 2014 +0000 @@ -26,18 +26,14 @@ ## arrival rate @math{\lambda}, individual service rate @math{\mu} ## and offered load @math{A = \lambda / \mu} has all servers busy. ## -## @iftex -## +## @tex ## @math{E_B(A, m)} is defined as: ## -## @tex ## $$ ## E_B(A, m) = \displaystyle{{A^m \over m!} \left( \sum_{k=0}^m {A^k \over k!} \right) ^{-1}} ## $$ ## @end tex ## -## @end iftex -## ## @strong{INPUTS} ## ## @table @var
--- a/main/queueing/inst/erlangc.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/erlangc.m Sat Mar 08 15:55:05 2014 +0000 @@ -21,37 +21,32 @@ ## ## @cindex Erlang-C formula ## -## Compute the steady-state probability that an open queueing system -## with @math{m} identical servers, infinite wating space, arrival rate -## @math{\lambda}, individual service rate @math{\mu} and offered load -## @math{A = \lambda / \mu} are busy. This probability is also called -## Erlang-C formula @math{E_C(A, m)}. -## -## @iftex +## Compute the steady-state probability @math{E_C(A, m)} that an open +## queueing system with @math{m} identical servers, infinite wating +## space, arrival rate @math{\lambda}, individual service rate +## @math{\mu} and offered load @math{A = \lambda / \mu} has all the +## servers busy. ## +## @tex ## @math{E_C(A, m)} is defined as: ## -## @tex ## $$ ## E_C(A, m) = \displaystyle{ {A^m \over m!} {1 \over 1-\rho} \left( \sum_{k=0}^{m-1} {A^k \over k!} + {A^m \over m!} {1 \over 1 - \rho} \right) ^{-1}} ## $$ -## @end tex ## ## where @math{\rho = A / m = \lambda / (m \mu)}. -## -## @end iftex +## @end tex ## ## @strong{INPUTS} ## ## @table @var ## -## @item A -## Offered load, defined as @math{A = \lambda / \mu} where +## @item A Offered load. @math{A = \lambda / \mu} where ## @math{\lambda} is the mean arrival rate and @math{\mu} the mean ## service rate of each individual server (real, @math{0 < A < m}). ## -## @item m -## Number of identical servers (integer, @math{m @geq{} 1}). Default @math{m = 1} +## @item m Number of identical servers (integer, @math{m @geq{} 1}). +## Default @math{m = 1} ## ## @end table ## @@ -59,8 +54,7 @@ ## ## @table @var ## -## @item B -## The value @math{E_C(A, m)} +## @item B The value @math{E_C(A, m)} ## ## @end table ##
--- a/main/queueing/inst/qncmmvaap.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qncmmvaap.m Sat Mar 08 15:55:05 2014 +0000 @@ -34,11 +34,9 @@ ## ## This implementation uses Bard and Schweitzer approximation. It is based ## on the assumption that -## @iftex ## @tex ## $$Q_i({\bf N}-{\bf 1}_c) \approx {n-1 \over n} Q_i({\bf N})$$ ## @end tex -## @end iftex ## @ifnottex ## the queue length at service center @math{k} with population ## set @math{{\bf N}-{\bf 1}_c} is approximately equal to the queue length
--- a/main/queueing/inst/qsmh1.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmh1.m Sat Mar 08 15:55:05 2014 +0000 @@ -26,11 +26,9 @@ ## throughput for a @math{M/H_m/1} system. In this system, the customer ## service times have hyper-exponential distribution: ## -## @iftex ## @tex ## $$ B(x) = \sum_{j=1}^m \alpha_j(1-e^{-\mu_j x}),\quad x>0 $$ ## @end tex -## @end iftex ## ## @ifnottex ## @example
--- a/main/queueing/inst/qsmm1.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmm1.m Sat Mar 08 15:55:05 2014 +0000 @@ -23,19 +23,17 @@ ## ## Compute utilization, response time, average number of requests and throughput for a @math{M/M/1} queue. ## -## @iftex +## @tex ## The steady-state probability @math{\pi_k} that there are @math{k} ## jobs in the system, @math{k \geq 0}, can be computed as: ## -## @tex ## $$ ## \pi_k = (1-\rho)\rho^k ## $$ -## @end tex ## ## where @math{\rho = \lambda/\mu} is the server utilization. ## -## @end iftex +## @end tex ## ## @strong{INPUTS} ##
--- a/main/queueing/inst/qsmm1k.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmm1k.m Sat Mar 08 15:55:05 2014 +0000 @@ -27,17 +27,16 @@ ## requests in the system is @math{K}, and the maximum queue length is ## @math{K-1}. ## -## @iftex +## @tex ## The steady-state probability @math{\pi_k} that there are @math{k} ## jobs in the system, @math{0 @leq{} k @leq{} K}, can be computed as: ## -## @tex ## $$ ## \pi_k = {(1-a)a^k \over 1-a^{K+1}} ## $$ -## @end tex +## ## where @math{a = \lambda/\mu}. -## @end iftex +## @end tex ## ## @strong{INPUTS} ##
--- a/main/queueing/inst/qsmminf.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmminf.m Sat Mar 08 15:55:05 2014 +0000 @@ -27,16 +27,14 @@ ## ## @cindex @math{M/M/}inf system ## -## @iftex +## @tex ## The steady-state probability @math{\pi_k} that there are @math{k} ## requests in the system, @math{k @geq{} 0}, can be computed as: ## -## @tex ## $$ ## \pi_k = {1 \over k!} \left( \lambda \over \mu \right)^k e^{-\lambda / \mu} ## $$ -## @end tex -## @end iftex +## @end tex ## ## @strong{INPUTS} ##
--- a/main/queueing/inst/qsmmm.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmmm.m Sat Mar 08 15:55:05 2014 +0000 @@ -27,30 +27,26 @@ ## with @math{m} identical servers connected to a single FCFS ## queue. ## -## @iftex +## @tex ## The steady-state probability @math{\pi_k} that there are @math{k} ## jobs in the system, @math{k \geq 0}, can be computed as: ## -## @tex ## $$ ## \pi_k = \cases{ \displaystyle{\pi_0 { ( m\rho )^k \over k!}} & $0 \leq k \leq m$;\cr ## \displaystyle{\pi_0 { \rho^k m^m \over m!}} & $k>m$.\cr ## } ## $$ -## @end tex ## ## where @math{\rho = \lambda/(m\mu)} is the individual server utilization. ## The steady-state probability @math{\pi_0} that there are no jobs in the ## system can be computed as: ## -## @tex ## $$ ## \pi_0 = \left[ \sum_{k=0}^{m-1} { (m\rho)^k \over k! } + { (m\rho)^m \over m!} {1 \over 1-\rho} \right]^{-1} ## $$ +## ## @end tex ## -## @end iftex -## ## @strong{INPUTS} ## ## @table @var
--- a/main/queueing/inst/qsmmmk.m Wed Mar 05 22:53:37 2014 +0000 +++ b/main/queueing/inst/qsmmmk.m Sat Mar 08 15:55:05 2014 +0000 @@ -31,31 +31,27 @@ ## is @math{K-m}. This function generates and ## solves the underlying CTMC. ## -## @iftex +## @tex ## ## The steady-state probability @math{\pi_k} that there are @math{k} ## jobs in the system, @math{0 @leq{} k @leq{} K} can be expressed as: ## -## @tex ## $$ ## \pi_k = \cases{ \displaystyle{{\rho^k \over k!} \pi_0} & if $0 \leq k \leq m$;\cr ## \displaystyle{{\rho^m \over m!} \left( \rho \over m \right)^{k-m} \pi_0} & if $m < k \leq K$\cr} ## $$ -## @end tex ## ## where @math{\rho = \lambda/\mu} is the offered load. The probability ## @math{\pi_0} that the system is empty can be computed by considering ## that all probabilities must sum to one: @math{\sum_{k=0}^K \pi_k = 1}, ## which gives: ## -## @tex ## $$ ## \pi_0 = \left[ \sum_{k=0}^m {\rho^k \over k!} + {\rho^m \over m!} \sum_{k=m+1}^K \left( {\rho \over m}\right)^{k-m} \right]^{-1} ## $$ +## ## @end tex ## -## @end iftex -## ## @strong{INPUTS} ## ## @table @var