a=0.7;d1=0.5;d2=0.2;

totalD = d1+d2

rBit[prob_]:=If[RandomReal[]≤prob,1,0]

uProb=0.5;

control[{x1_,x2_}]:=rBit[uProb] (*1 implies joining queue 1 and 0 implies joining queue 2*)

control[{x1_,x2_}]:=If[x1≤ x2, 1,0]

nextState[{x1_,x2_}]:=Module[{},
arr=rBit[a];
ctrl=control[{x1,x2}];
AA=If[arr==0,{0,0},{ctrl,1-ctrl}];
DD={rBit[d1],rBit[d2]};
LL={Max[DD[[1]]-(x1+AA[[1]]),0],
Max[DD[[2]]-(x2+AA[[2]]),0]};
 {x1,x2}+AA-DD+LL
]

traj=NestList[nextState,{10,10},30000];

Manipulate[ListPlot[Take[traj,nn],AxesOrigin->{0,0},Joined->True,PlotRange->{{0,200},{0,200}}],
{nn,1,Length[traj],1}]