Through the method of queuing theory

a mathematical model of the queuing of continuous casting billets at cast-rolling interface of the billet straight rolling process is constructed

and a case analysis of the queuing theory is carried out on the billet straight rolling production line of 2 × 70 t EAF-6 strand 150 mm × 150 mm billet at a steel mill. On the premise of ensuring the direct rolling rate

the output of the production line increases by optimizing the direct rolling process

and the liquid steel quantity increases from 1.88 t/min to 2.3 t/min. In the billet direct rolling production system

the shorter the average waiting time of continuous casting billet

the higher the efficiency of direct rolling production at the production line ； In order to maximize the output of the straight rolling process

it is necessary to satisfy the same amount of steel in the continuous casting process and the rolling process. In order to achieve the highest straight rolling efficiency

that is

the largest straight rolling rate

the average waiting time of the continuous casting slab in the queuing system needs to be less than the limit waiting time of the casting slab. Only when the above two conditions are met at the same time

the casting-rolling connection matching of the billet straight rolling process is optimal.