How should a traveler pray if he experiences a discharge of madhiy and is with many other travelers, and is it permissible for him to perform tayammum or must he perform wudu, knowing that he is unable to perform ghusl?

The fluid mentioned by the questioner is madhy (pre-seminal fluid), which is impure by scholarly consensus. It does not necessitate a full body bath (ghusl) like maniyy (seminal fluid). Rather, it requires washing the entire male organ and sprinkling water on whatever part of the garment or body it touched before prayer. What was mentioned is not considered an excuse to forgo washing this impurity. However, if one is unable to wash it, they must perform ablution (wudu’) and pray due to the sanctity of the time, then repeat the prayer when they are able to wash it, because removing impurity from the body and garment is a condition for the validity of prayer.