>1,MVS allow different task to have their own address space.While the
number of address space increases in system,the total amount of virtual
storage can become very big. 
>However,as I know,virtual storage is supported by real storage and
auxiliary storage.With 31-bit addressing,the max size of real storage or
auxiliary storage is 2G.
>   So,the max size of virtual storage=max real storage+max auxiliary
storage=4G
>   Does this mean that the total size of all the address spaces cannot
exceed 4G although in theory each address space can have a max size of
2G?

>2,Take a TSO user's address space for example.Suppose its size is
5M.Whenthe user logon to tso,the address space is established which
means 5M virtual storage space is 
>allocated for this address space.So this 5M space is being mapped using
real storage plus auxiliary storage even if the user doesn't do any job
after logon?


Each address space has up to 2 GB available (not in use) which will
reside in a combination of real and auxiliary storage.  Therefore the
more address spaces running, the more real storage and auxiliary storage
is committed to support them.  If there are too many address spaces with
large virtual storage requirements, then real storage may be
over-committed and require more movement of pages between real and
auxiliary storage.  In this case, the "benefit" of allowing more work in
the system is offset by the "cost" of moving storage between real and
auxiliary.  

The maximum size of virtual storage (in 31-bit mode) is always 2 GB
since that is the largest address that can be contained in 31-bits.
Similarly, that is the reason why there can be no more than 2 GB's of
real memory.  In 31-bit mode there is simply no way to hold an address
referencing anything larger.

Using your example of the TSO user's address space;  the 5MB only
represents a "potential" use and therefore essentially defines a limit
regarding how much virtual storage we're willing to allow this user to
access.  

In a nutshell, the virtual storage limit is based on the amount that a
user MIGHT allocate.  Based on what they allocate (i.e. actually use),
this translates into a requirement to hold these pages someplace; either
in real memory or auxiliary storage.  If all the virtual storage can't
be held in real memory, then a potential exists requiring storage to be
moved between real and auxiliary storage (i.e. paging).  There is
fundamentally no virtual storage limit regarding the number of address
spaces other than those imposed by the z/OS operating system itself
(which are based on boundaries regarding control block sizes).  However,
a practical limit is reached when the performance costs of moving pages
between real and auxiliary become greater than the benefit of running
that much concurrent work.  In principle, if you can tolerate it, then
you can do it.

Adam

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