On the time of the first level achievement for the ascending-descending process

We consider a stochastic process whose trajectories are characterized by alternate linear growth and linear decrease during time intervals of random length; the process can also keep its value during random intervals of time between growth and decrease. This process can be considered as a mathematical model of accumulation and consumption of materials, when random periods of time are combined for accumulation, spending and interruptions in operation. We study mean value $\mathbf{E} N$ of the first achievement time a fixed level for trajectories of this process, including finding exact formulas for $\mathbf{E} N$, estimating from above with an inequality and obtaining the asymptotics of $\mathbf{E} N$ under an infinitely receding level.