function [R,P] = cmpt_P_and_R(lambdaRequests,lambdaReturns,max_n_cars,max_num_cars_can_transfer) % % Notes: checked 2007-12-10 (no mistakes found) % % Written by: % -- % John L. Weatherwax 2007-12-03 % % email: wax@alum.mit.edu % % Please send comments and especially bug reports to the % above email address. % %----- if( nargin==0 ) lambdaRequests=4; lambdaReturns=2; max_n_cars=20; max_n_cars_can_transfer=5; end PLOT_FIGS=0; % the number of possible cars at any site first thing in the morning: nCM = 0:(max_n_cars+max_num_cars_can_transfer); % return the average rewards: R = zeros(1,length(nCM)); for n = nCM, tmp = 0.0; for nr = 0:(10*lambdaRequests), % <- a value where the probability of request is very small. tmp = tmp + 10*min(n,nr)*poisspdf( nr, lambdaRequests ); end R(n+1) = tmp; end if( PLOT_FIGS ) figure; plot( nCM, R, 'x-' ); grid on; axis tight; xlabel(''); ylabel(''); drawnow; end % return the probabilities: P = zeros(length(nCM),max_n_cars+1); for nreq = 0:(10*lambdaRequests), % <- a value where the probability of request is very small. reqP = poisspdf( nreq, lambdaRequests ); % for all possible returns: for nret = 0:(10*lambdaReturns), % <- a value where the probability of returns is very small. retP = poisspdf( nret, lambdaReturns ); % for all possible morning states: for n = nCM, sat_requests = min(n,nreq); new_n = max( 0, min(max_n_cars,n+nret-sat_requests) ); P(n+1,new_n+1) = P(n+1,new_n+1) + reqP*retP; end end end if( PLOT_FIGS ) figure; imagesc( 0:max_n_cars, nCM, P ); colorbar; xlabel('num at the end of the day'); ylabel('num in morning'); axis xy; drawnow; end