From: arne@vajhoej.dk   
      
   On 11/12/2025 2:54 PM, Arne Vajhøj wrote:   
   > On 11/11/2025 10:56 PM, Lawrence D’Oliveiro wrote:   
   >> As for the rest, it doesn’t matter if a box falls over every minute, or a   
   >> hard drive crashes every few minutes; they have higher-level redundancy   
   >> and recovery procedures that can routinely recover from all those   
   >> failures, without the users ever noticing.   
   >>   
   >> No mainframe can match that.   
   >   
   > Of course mainframes can match that.   
   >   
   > The fundamental mechanism is the same for mainframes and   
   > let us call it modern distributed environments.   
   >   
   > You need N systems running to handle load. There is   
   > a probability Pd of one system becoming unavailable.   
   > You want Pr probability of handling the load.   
   >   
   > You can calculate how many systems M you need to   
   > achieve that.   
   >   
   > N is smaller, Pd is smaller and the cost of a   
   > system is much bigger for mainframes than for   
   > x86-64 servers.   
   >   
   > But the formula is the same. You can do the math.   
      
   If we take the simple case of N = 1 then:   
      
   M = ceil(log(1 - Pr)/ log(Pd))   
      
   make it happen.   
      
   If Pr = 0.99999 then:   
      
   Pd = 0.1 => M = 5   
   Pd = 0.01 => M = 3   
   Pd = 0.001 => M = 2   
   Pd = 0.0001 => M = 2   
   Pd = 0.00001 => M = 1   
      
   Arne   
      
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