Problem definition and Analysis

Scope Performance indicators (system time, resource occupation, cost,...) Key object classes (order, delivery,...) and actions. Actions cause state change of objects. Necessary for understanding and modeling. Solution alternatives Problems to be addressed Account for expected future developments Define what to study (and what not). Too much = wasted work!

Objects and actions A citizen can be in various states: e.g. not involved, entered, being judged, being instructed, away for 2nd photo, back, being helped, finished. Servant's states: idle, judging, instructing, processing. Objects have a life cycle, consisting of states. For example, for the passport case, citizen and civil servant objects do matter. Passport actions? Ferry objects and actions?

Performance indicators Ferry case? Passport case: average lead time, standard deviation. maximum queue size (facilities). occupation rate of civil servant. Average lead time and standard deviation for A to B and for B to A cars.

Problems and solutions Ferry case? Passport case: Long queues (possibly, depending on demand) Solutions: approve more, skip judgement, appointment system Which new ferry to buy Consider future developments extrapolate trends beware special circumstances!

Analysis Parameters: - maximal capacity of key resource(s) -  : arrival intensity divided by capacity ( both measured in nr of cases per time unit) Analyze extreme cases: - small  -  almost 1 Capacity and intensity can be estimated or assumed.

Passport problem case: citizen needing document resource: civil servant Problem: long queues. Proposed solutions: - less strict judgement - oblige photo from preferred shop performance measured by system time (wait time + service time).

Passport analysis Passport/photo example: accept ratio a, with 0 < a < 1 average time to instruct photo remake: t average time to create document: u Average resource time needed for client: u + a.t (= waiting time in absence of queues) Average influx  clients per u + a.t time units.  ≥1: not enough resource capacity; infinite waiting time. Analyze extreme cases. Assuming M/M/1 queue (appendix F), we obtain an average service time of ( u + a.t) / ( 1 -  ).

M/M/1 passport queue time / ( u + a.t )

Passport case Simulation needed? Proposed solutions: - less strict judgement - oblige photo from preferred shop - introduce an appointment system Give comment on proposals Can you think of additional constraints that preclude the problem's analysis? Beware of tunnel vision!

Ferry problem case: car needing to cross resource: ferry Problem: new ferry needed Proposed alternatives: - faster, less cars - slower, more cars performance measured by system time (wait time + service time).

Ferry analysis Ferry example: cycle time: c; up to n ≥10 places per cycle (batch size) capacity: n/c cars per time unit Input:  (n/c) cars per time unit;  <1. Minimum average waiting time c/2. Processing: fixed time c /2. Low influx (e.g.  ≤ 0.3 ): negligible probability of more than n waiting cars. average system time c + .

Ferry queue time / c 

Two ferries are proposed. For ferry 1, cycle time c equals 6 minutes, n equals 10. For ferry 2, c equals 8 minutes and n equals 15. systime ferry 2 systime ferry 1 system time (minutes) intensity (cars per minute)

Standard deviation important for traffic studies. measured times: 5,11,13, 7,14; average: 10 measured times: 8,11,10, 9,12; average: 10 How do the two ferries compare w.r.t. stdev?

Ferry case Simulation needed? Give essential characteristics. M/D/1 queue with batches extra time for getting on/off Choice between alternatives depends on traffic intensity. Increase expected? Decision based on mean throughput time  and standard deviation . For only plm. 15% of cases, throughput time exceeds   .

Homework: Study chapter 3 and appendix F of lecture notes. Special attention to Little's formula and M/M/1. Assignment (individual, discussions encouraged): Write DCT report (2 pags A4), defining concepts pertaining to the case. Indicate a few promising solution strategies. Classwork/Homework Classwork: Exercises on page 6 and 10 of lecture notes. Analyze DCT case, pose additional questions, propose strategies. (give evidence by analysis) Mail to