Risk Assessment of a Stochastic Service System
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ISSN: 1004-3756 (paper), 1861-9576 (online) CN 11-2983/N
Risk Assessment of a Stochastic Service System Igor Lazov Faculty of Informatics, European University Skopje, 1000 Skopje, Macedonia [email protected] ()
Abstract. A stochastic service system of finite size M is comprised of identical service facilities, including
or not a waiting queue, which simultaneously treats N customers, N ∈ {0, 1, · · · , M}. Depending on the concepts of system information i and system entropy S E(i), we promote a risk assessment procedure. By definition, the system entropy is the uncertainty associated with the system, and the system expected loss is the risk associated with the system. Thus, accepting the system information as loss function, we can identify risk and uncertainty, associated with the system, using the entropy as risk function. Further, we differ risk of the system (i.e., risk observed by an outside observer), risk observed by an arriving customer, and risk observed by a departing customer, giving a separate expression for each one. Then, these risks are compared with each other, when the system has the same average number E(N) of customers seen by any viewpoint. The three risk types (together with the three customer means) allow us to distinguish two systems obeying the same probability distribution. This approach enables system operators to choose suitable values for system utilization and size, in view of the three risks ratio. The developed procedure is applied to the information linear system, Erlang loss system, single-server queueing system with discouraged arrivals, Binomial system and Engset loss system. Keywords: Absolute and relative risk, uncertainty, system information and entropy, system utilization, stochastic service system
1. Introduction A stochastic service system with finite size consists of a finite number of simultaneously reserved elements. It constitutes a homogenous group of identical channels (e.g. servers, trunks, agents, etc.) working in parallel, including or not a waiting queue. An arriving customer is accepted for service if at least one channel is idle (i.e., unoccupied). The customer, which is not served immediately is queued in the system (queueing system), or blocked by the system (loss system). Typical examples might be: 1) banks/markets - waiting for service, 2) computers - waiting for a response, 3) manufacturing - waiting for a job on machines, 4) public transport - waiting for a train or a bus, etc. For instance, in telephony, the blocked calls are rerouted to another group, placed in a queue, or played back a tone or announcement. So, they result in differences
in the traffic load. Also, the system blocking can be considered as: 1) time blocking, which refers to the proportion of time the system spends in the blocking state; 2) call blocking, the proportion of arriving calls which are blocked; and 3) traffic blocking, the ratio of the traffic intensity of the blocked traffic to that of the offered traffic. All these quantities are equal if the arrival process is Poisson and service ti
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