COURSE: INDUSTRIAL ENGINEERING LESSON: REPRESENTATION OF QUEU NG MODEL
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REPRESENTATION OF QUEU NG MODEL Queuing model are normally represented by Kendall and Lee' notations whose general formula is (a/b/c): (d/e/t1) Where a arrival pattern b-- service pattern c-number of serve d service rule or discipline e maximum number of customers allowed in system fcalling population or source
REPRESENTATION OF QUEU NG MODEL Symbol for a & b: M Markovian (M) (Poisson) for arrival or exponential service line GI General Independent arrival distribution E = Erlangan or Gamma Distribution D = Deterministic Inter Arrival or service Time Symbol for c: 1,2,3,4.. Symbol for d: FIFO or FCFS, LIFO, SIRO Symbol for e and f:N--finite, nfinte
EXAMPLE - (M/M/): (FIFO/o/o) This notation denotes queuing model in which arrivals are Poisson distributed, exponential service time in a single server,the size of system and calling population is infinite and the service rule is First In First Out
IMPORTANT TERMS 2. Example-o cust h a lo /d= Sesvice Rake. (Exponential) 15 cust ms lates-Sevice time-_-_.Ymin/cust stem oodes F.B
IMPORTANT TERMS A) System Utilisation Utilisation Factor Channel Efficiency Clearing Ratio Percentage Utilisation Percentage time server is busy Probability that a customer has to wait
IMPORTANT TERMS B) Probability that the system is idle or probability of zero customer in the system or probability that a customer does not have to wait in the queue. Pa S
IMPORTANT TERMS C) Probability of having exactly 'n' customers in the system + 00
IMPORTANT TERMS D) Average number of customers in the system = average number of customers being served + those waiting in the queue I- S