Linq - how get the minimum, if value = 0, get the next value - sql-server

Question

I have a test database which logs data from when a store logs onto a store portal and how long it stays logged on.
Example:
(just for visualizing purposes - not actual database)
Stores
Id Description Address City
1 Candy shop 43 Oxford Str. London
2 Icecream shop 45 Side Lane Huddersfield
Connections
Id Store_Ref Start End
1 2 2011-02-11 09:12:34.123 2011-02-11 09:12:34.123
2 2 2011-02-11 09:12:36.123 2011-02-11 09:14:58.125
3 1 2011-02-14 08:42:10.855 2011-02-14 08:42:10.855
4 1 2011-02-14 08:42:12.345 2011-02-14 08:50:45.987
5 1 2011-02-15 08:35:19.345 2011-02-15 08:38:20.123
6 2 2011-02-19 09:08:55.555 2011-02-19 09:12:46.789
I need to get various data from the database. I've already gotten the max and average connection duration. (So probably very self-evident that..) I also need to have some information about which connection lasted the least. I ofcourse immediately thought of the Min() function of Linq, but as you can see, the database also includes connections that started and ended instantly. Therefore, that data isn't actually "valid" for data analysis.
So my question is how to get the minimum value, but if the value = 0, get the next value that is the lowest.
My linq query so far (which implements the Min() function):
var min = from connections in Connections
join stores in Stores
on connections.Store_Ref equals stores.Id
group connections
by stores.Description into groupedStores
select new
{
Store_Description = groupedStores.Key,
Connection_Duration = groupedStores.Min(connections =>
(SqlMethods.DateDiffSecond(connections.Start, connections.End)))
};
I know that it's possible to get the valid values through multiple queries and/or statements though, but I was wondering if it's possible to do it all in just one query, since my program expects linq queries to be returned and my preference goes to keeping the program as "light" as possible.
If you have to great/simple method to do so, please share it. Your contribution is very appreciated! :)

Answer 1

What if you add, before the select new, a let clause for the duration of the conection with something like:
let duration = SqlMethods.DateDiffSecond(connections.Start, connections.End)
And then add a where clause
where duration != 0

Answer 2

var min = from connections in Connections.Where(connections => (SqlMethods.DateDiffSecond(connections.Start, connections.End) > 0)
join stores in Stores
on connections.Store_Ref equals stores.Id
group connections
by stores.Description into groupedStores
select new
{
Store_Description = groupedStores.Key,
Connection_Duration = groupedStores.Min(connections =>
(SqlMethods.DateDiffSecond(connections.Start, connections.End)))
};
Try this, With filtering the "0" values you will get the right result, at least that is my taught.

Answer 3

Include a where clause before calculating the Min value.
groupedStores.Where(conn => SqlMethods.DateDiffSecond(conn.Start, conn.End) > 0)
.Min(conn => (SqlMethods.DateDiffSecond(conn.Start, conn.End))