A proper edget-coloring of a graphGis a coloringof edges ofGwith colors 1,2,:::,tsuch that all colors are used,and no two adjacent edges receive the same color. The set of colorsof edges incident with a vertexxis called a spectrum ofx. Anynonempty subset of consecutive integers is called an interval. Aproper edget-coloring of a graphGis interval in the vertexxif thespectrum ofxis an interval. A proper edget-coloringφof a graphGis interval on a subsetR0of vertices ofG, if for anyx∈R0,φisinterval inx. A subsetRof vertices ofGhas ani-property if thereis a proper edget-coloring ofGwhich is interval onR. IfGis agraph, and a subsetRof its vertices has ani-property, then theminimum value oftfor which there is a proper edget-coloring ofGinterval onRis denoted bywR(G). We estimate the value of thisparameter for biregular bipartite graphs in the case whenRis oneof the sides of a bipartition of the graph.