  We study routing games where every agent sequentially decides her next edge
when she obtains the green light at each vertex. Because every edge only has
capacity to let out one agent per round, an edge acts as a FIFO waiting queue
that causes congestion on agents who enter. Given $n$ agents over $|V|$
vertices, we show that for one agent, approximating a winning strategy within
$n^{1-\varepsilon}$ of the optimum for any $\varepsilon>0$, or within any
polynomial of $|V|$, are PSPACE-hard. Under perfect information, computing a
subgame perfect equilibrium (SPE) is PSPACE-hard and in FPSPACE. Under
imperfect information, deciding SPE existence is PSPACE-complete.
