There is no legislation in Germany how long you have to wait in such a situation.
First let's look what happened:
According to your work contract, you are obligated to be available for work and follow the directions of your employer. Let's not go into nuances of the latter duty, because they depend on what type of work you are doing. Your employer is obligated to pay you if you fulfill your duties.
What happened is called Annahmeverzug (default of acceptance) in German civil law (§ 615 BGB):
Kommt der Dienstberechtigte mit der Annahme der Dienste in Verzug, so
kann der Verpflichtete für die infolge des Verzugs nicht geleisteten
Dienste die vereinbarte Vergütung verlangen, ohne zur Nachleistung
verpflichtet zu sein. Er muss sich jedoch den Wert desjenigen
anrechnen lassen, was er infolge des Unterbleibens der Dienstleistung
erspart oder durch anderweitige Verwendung seiner Dienste erwirbt oder
zu erwerben böswillig unterlässt. …
English translation: If the person entitled to services is in default in accepting the services, then the party owing the services may demand the agreed remuneration for the services not rendered as the result of the default without being obliged to provide cure. However, he must allow to be credited against him what he saves as a result of not performing the services or acquires or wilfully fails to acquire through use of his employment elsewhere. …
If your employer doesn't enable you to work, they have to pay you for your time. You don't have to make up that time. If you save money by not working or had the opportunity to earn money by other means1 during that time, this can be deducted from your pay.
Now, the question is how you fulfill your duty of being available for work. This depends on the specifics and really can only be answered by a lawyer or court (and IANAL). You do not need to endure hardships but have to accept reasonable inconveniences. Thus, you can leave if waiting becomes more than an inconvenience (usually that will be caused by weather or by bodiliy functions). If you leave, you should still be available for work unless that becomes unreasonable, e.g., because you could use that time to earn money by other means.
1 Usually, it can be safely assumed that you don't have that opportunity. However, a daytaler might easily have that opportunity.