Availability analysis of banking server with warm standby

Introduction

In banking industry all the data relating to transaction history along with authorization is stored in local sever (Bank branch) and stand-by remote server. As data in baking industry is very important for customers and the management, daily data and transaction history of a branch are stored in the branch and also by the manager of the branch in the hard disc at the time of closing daily/regularly. Considering the importance of individual units in system Kumar, J. & Malik, S. C. [1] have discussed the concept of preventive maintenance for a single unit system. Liu., R. [2] , Malik, S. C. [3] , Nakagawa, T. and Osaki, S. [4] have discussed reliability analysis of a one unit system with un-repairable spare units and its applications. Goel, P. & Singh J. [5] , Gupta, P., Singh, J. & Singh, I.P. [6] , Kumar, S. & Goel, P. [7] , Gupta, V. K. [8] , Chaudhary, Goel & Kumar [9] Sharma & Goel [10] , Ritikesh & Goel [11] and Goyal & Goel [12] have discussed behavior with perfect and imperfect switch-over of systems using various techniques. All the transaction history is stored in the remote server simultaneously because in case of failure of local server data may be retrieved from the remote server. The failure rate of local server is much higher than that of the remote server which may be due to poor local environmental conditions such as electricity failure, earth quake, inefficient data operator and other local conditions. Remote server has better maintenance and environmental conditions as the data of all branches stored in the remote server. The management maintains better environment conditions of remote server, hence the failure rates of local server are higher than that of remote server and repair rates of local server is poor than that of remote server. On failure of local server data is retrieved from the remote server for the smooth functioning of the banking industry i.e. remote server works as warm stand to local server. Taking constant failure rates & repair rates with remote server as standby to local server a transition diagram of the system is drawn. The system consists of local server 'A' and standby remote server 'B'. There may be times when some of the banking operations may not be carried out by A or B, then the system works in reduced capacity. If the failure rate of local server 'A' to reduced state is λ1, and from reduced state to failed state is λ2 and repair rate of local server from reduced state to A is w2 and from failed state to reduce state is w1 similarly for the remote server B with failure rates λ3, λ4 and repair rates w4 and w3. It is assumed that when any of servers fails then the system is not put to use. Fuzzy concept is used to determine failure/working state of a unit. Taking failure rates exponential, repair rates general & independent and taking into consideration various probabilities, a transition diagram of the system is developed to find Primary circuits, Secondary circuits & Tertiary circuits and Base state. Problem is solved using RPGT to determine system parameters. System behavior is discussed with the help of graphs and tables. Particular cases for arm, cold and hot standby cases are taken to study the effect of failure and repair rates on system parameters. Tables and Graphs are drawn to compare the results.

Assumptions and Notations

The following assumptions and notations are taken: -1. A single repair facility is available.

2. The distributions of failure times and repair times are exponential and general respectively and also different.

3. Failures and repairs are statistically independent. 4. Repair is perfect and repaired system is as good as new one. 5. Nothing can fail when the system is in failed state. 6. The system is discussed for steady-state conditions. 7. Replacement of Un-repairable unit and repair facility is immediate. 8. There are separate repairmen for local and remote servers.

: A circuit formed through un-failed states. m-cycle: A circuit (may be formed through regenerative or non-regenerative / failed state) whose terminals are at the regenerative state m.

: A circuit (may be formed through un-failed regenerative or non-regenerative state) whose terminals are at the regenerative m state.

: r-th directed simple path from i-state to j-state; r takes positive integral values for different paths from i-state to j-state.

: A directed simple failure free path from -state to i-state. Vm,m: Probability factor of the state m reachable from the terminal state m of the m-cycle.

: Probability factor of the state m reachable from the terminal state m of the . Ri (t): Reliability of the system at time t, given that the system entered the un-failed Regenerative state 'i' at t = 0. Ai (t)

: Probability of the system in up time at time 't', given that the system entered Regenerative state 'i' at t = 0. Bi (t)

: Reliability that the server is busy for doing a particulars job at time 't'; given That the system entered regenerative state 'i' at t = 0. Vi (t)

: The expected no. of server visits for doing a job in (o,t] given that the system Entered regenerative state 'i' at t = 0. ',' denote derivative Wi (t): Probability that the server is busy doing a particular job at time t without transiting to any other regenerative state 'i' through one or more non-regenerative states, given that the system entered the regenerative state 'i' at t = 0. μi: Mean sojourn time spent in state i, before visiting any other states; =: The total un-conditional time spent before transiting to any other regenerative states, given that the system entered regenerative state 'i' at t=0. Ni: Expected waiting time spent while doing a given job, given that the system entered regenerative state 'i' at t=0; (0,1) (0,2) (0,1,3) (0,2,4)

(0,2,0) (0,2,4,0) (0,2,0) (0,2,4,0)

Nil Nil Nil From the table 2, we see that at working state '0' there are maximum number of primary circuits, hence state '0' is the base state. Primary, Secondary, Tertiary Circuits w. r. t. the Simple Paths (Base-State '0')

References

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