public string GetSelectedTabPage(
    string tabContainerName
)

Public Function GetSelectedTabPage(
    tabContainerName As String
) As String

using DevExpress.DashboardCommon;
using System.Linq;
// ...

enum NextPrevValue {
    Next,
    Prev
}

void ShowNextPrevTab(NextPrevValue value) {
    Dashboard dashboard = dashboardViewer.Dashboard;
    TabContainerDashboardItem tabContainer = dashboard.Items.SingleOrDefault(i => i is TabContainerDashboardItem) as TabContainerDashboardItem;
        if(tabContainer != null) {
            int increment = value == NextPrevValue.Next ? 1 : -1;
            string tabContainerName = tabContainer.ComponentName;
            int selectedIndex = dashboardViewer.GetSelectedTabPageIndex(tabContainerName);
            int pageCount = tabContainer.TabPages.Count;
            dashboardViewer.SetSelectedTabPage(tabContainerName, (selectedIndex + pageCount + increment) % pageCount);
        }
}

Imports DevExpress.DashboardCommon
Imports System.Linq
' ...

Friend Enum NextPrevValue
    [Next]
    Prev
End Enum

Private Sub ShowNextPrevTab(ByVal value As NextPrevValue)
    Dim tabContainer As TabContainerDashboardItem = TryCast(dashboard.Items.SingleOrDefault(Function(i) TypeOf i Is TabContainerDashboardItem), TabContainerDashboardItem)
    If tabContainer IsNot Nothing Then
        Dim increment As Integer = If(value = NextPrevValue.Next, 1, -1)
        Dim tabContainerName As String = tabContainer.ComponentName
        Dim selectedIndex As Integer = dashboardViewer.GetSelectedTabPageIndex(tabContainerName)
        Dim pageCount As Integer = tabContainer.TabPages.Count
        dashboardViewer.SetSelectedTabPage(tabContainerName, (selectedIndex + pageCount + increment) Mod pageCount)
    End If
End Sub