This page contains some articles about the planning, crewing, movement and control of trains. It is not concerned with the type of trains except as how this might affect operation. It is based on modern practice around the world, showing some examples where suitable. It is not concerned with signalling except where it is used to control trains.
More information on particular train operations is at:
Definitions - The Objectives - Locomotive Hauled Trains - Terminal Operations - Multiple Unit Operation - Push Pull Operation - High Speed Multiple Units - Headway - Terminals, Loops and Turnbacks - Train Service Planning - Round Trip Time - Train Loading - Rolling Stock Pages Calculations - Rolling Stock Pages Operation - Stock Balance - Working Timetable - Diagrams - Timekeeping - Recovery Time - Terminal Occupation - Stepping Back - Double-Ending - Train Crews - Crew names - Crew Hours and Numbers
First, it is important to set out some definitions. A train is defined here as one or more railway vehicles capable of being moved. It may consist of a locomotive (sometimes more than one) to provide power with various unpowered vehicles attached to it. It may consist of a multiple unit, i.e. several vehicles formed into a fixed formation or set, which carry their own power and do not require a locomotive. A train may be only a locomotive running light (deadheading) to a point elsewhere on the railway. A train may be passenger carrying, freight or, rarely nowadays, mixed.
A train may be manually driven (by a driver, operator or engineer) and may have other crew members (assistant driver, fireman, conductor and catering staff) to assist the driver and/or the passengers.
A train is an expensive piece of kit. A locomotive now costs about US$ 5 million and a coach up to US$ 1 million depending on the type. A multiple unit (i.e. a self-powered train without a locomotive) can cost an average of US$ 1.5 million for each vehicle, depending on type and size of order. This is a lot of capital to invest and it is essential to make sure it earns its keep. Trains sitting in stations and sidings may look nice but they don't earn money.
Crews are also expensive. They too, must be used efficiently and safely, which means regulating their hours but they will be needed to match the times that they are required on the trains. Allocation of crews is a scientific skill just as important as train control. For more information see Train Crews.
The infrastructure of a railway is its most expensive asset. A new railway can cost US$ 25 million per kilometre and this price will double to US$50 million for an elevated urban line. An underground metro or subway can cost up to US$200 million a kilometre in a country where protection against typhoons and earthquakes is required. See Railway Finance for more information on costs. Maximisation of the use of the line of route is essential and train operations management will play an important part.
The objective of good train operations management is to use the route, the rolling stock and crews in the most effective way. This is what this page attempts to explain.
Locomotive Hauled Trains
The traditional train comprises a collection of coaches (or freight wagons) with suitable motive power attached in the form of a locomotive. The train is made up of sufficient vehicles to carry the traffic offering and provided with enough power for the job. For passenger operations, one locomotive is usually sufficient. In heavy freight operations, this number might go up to four locomotives on the front and at some other places along the train.
A good deal of flexibility is possible with locomotive haulage. As long as the train weight remains within the capacity of the locomotive(s), any number of vehicles can be attached, although limits will be imposed by platform or siding lengths. Locomotives themselves can also be flexible, many being designed to cover a range of duties.
The advantages for locomotive hauled trains mean they are the best option for many railway operators around the world, particularly freight but, where traffic is dense, i.e. where a large number of trains are required, a more rational approach is necessary, particularly at terminals. In addition, in very predictable operations like commuter services or metro lines, fixed formation trains will be the most efficient.
One disadvantage of traditional locomotive haulage shows up at the end of the line. When a train arrives at a dead end terminal, the locomotive is trapped between the train and the buffer stops. The only way to release the locomotive is to remove the train and for that, a second locomotive is required. This second loco is attached to the other end of the train and will be used to provide power for the return trip. When the train has been removed, the first locomotive is released, moved away from the platform to a "loco siding" near the terminus and stored until used for the return trip of another train. This problem can be solved, if space is available. The train stops a distance from the buffer stops and a crossover to a run-around track is provided. This is sometime referred to as a "locomotive escape" and is used as shown in the diagram below.
Often, the adjacent platform track is used but it must be kept free of other trains. Sometimes a scissors crossover is used. Of course, the arrangement would not nowadays be suitable for a major city terminus where space is at a premium and land is very expensive, so efforts are made to use tracks to the optimum. So, although locomotive changing operations at terminals were, and still are commonplace, where there is intense traffic, additional movements for loco changing can restrict the terminal capacity. Also additional locomotives are required to cover these terminal operations. To overcome all these limitations, the Multiple Unit was introduced.
Multiple Unit Operation
Locomotive operation of intensive services was rapidly phased out when electric traction, using "multiple unit" operation, was introduced late last century for US urban railway lines. Within ten years the idea had spread to Europe. The facility for the electric traction system to be spread out along the train, compared with cramming it all together into a bulky locomotive, allowed a number of small power units to be distributed underneath the floors of several vehicles in the train. They were all simultaneously controlled by the driver in the leading car through wires running the length of the train. Thus was born the electric multiple unit or EMU. In later years, DMUs (diesel multiple units) were developed using the same principles.
A modern passenger multiple unit train is now made up of a number of inter-dependent vehicles which cannot operate unless all the vehicles are of the right type and are coupled in the correct position in the train. Power and auxiliary equipment is usually distributed under more than one vehicle and is all controlled from the driving position. Vehicles in multiple units are usually referred to as "cars" and are known as "motor cars" if powered and "trailer cars" if not.
Multiple unit trains are formed into "units" or "sets"of two or more cars. They are often semi-permanently coupled together, only being uncoupled inside a workshop for heavy maintenance. Units can operate singly - providing driver's cabs are provided at both ends - or coupled to form longer trains. Some operations require two (or more) multiple units to be coupled together to provide sufficient capacity for a particular service. This also allows trains to be lengthened or shortened whilst in service by adding or cutting units.
Some multiple unit trains are designed so that a unit has a full driver's cab at one end only. At least two units, coupled back to back, are required to make up a train for service. In the US, a development of this type of formation, known as "married pairs", has been popular since the 1960s. Two cars, coupled together and electrically dependent on each other, form a unit and a number of these are coupled to form trains of four, six, eight etc. cars. Similar formations have since appeared elsewhere, e.g. London Underground's Central Line.
Multiple unit trains are mainly used for high density suburban operations where traffic levels are easily predicted and form constant patterns which allows fixed train formations. In recent years, long distance traffics have shown the same tendency and many railways are now adopting the multiple unit formation for these routes - e.g. the French TGV, the UK HST, the Japanese Shinkansen.
Other advantages of the EMU are that it doesn't have to carry its own fuel, it takes it from overhead wires or an additional (third) rail and it is quick and simple to reverse at terminals. All you have to do was provide drivers controls at both ends of the train, connect them to the train wires and give the driver a key to switch in the controls at the end he wants to use. Locomotive changing is instantly eliminated, terminal space is released and trains can be turned round more quickly. All the driver has to do now is change ends.
Another form of multiple unit operation was adopted in the early 1960s when a new concept appeared called push-pull.
Push-pull operation was really only an adaption of the multiple unit principle but applied to a locomotive powered train. Assuming a regular level of traffic and an even interval service was required, trains could be formed with a locomotive at one end and a driving cab on the coach at the other end. If you could find a way of doing it cheaply by converting existing coaches, it could represent a big step forward. See Development of Push Pull Operation in the UK by Chris Grace.
The idea has now been adopted world-wide in two forms. One, as stated above, uses a locomotive at one end and a coach equipped with a driver's cab at the other end. The number of vehicles in between them may be varied seasonally if required but the formation is not normally varied on a train by train basis. In the UK, the coach at the rear has become designated a Driving Van Trailer (DVT). It is used to carry luggage and passengers are not permitted to ride in it at speeds over 160 km/h.
The second push-pull form uses two locomotives, one at each end of the train. This was applied to the Channel Tunnel "Le Shuttle" trains and has also appeared elsewhere, notably in Taiwan. The two locomotives are necessary in these cases to provide sufficient power.
High Speed Multiple Units
The modern two-locomotive concept for push-pull operation first appeared in 1959 with the UK's Blue Pullman series of trains. A diesel power car was provided at each end of a six- or eight-coach set. The concept was further developed in the 1970s with the UK High Speed Train (known as the HST) and in France with the TGV (Train à Grande Vitesse). The former is diesel powered, the latter electric but the concept is the same. Both these trains employ a power unit at each end with a set of passenger carrying coaches in-between. The Germans have joined the club with their ICE train. The only real difference between these trains and the original push-pull concept is that the newer trains were purpose built.
Not forgetting the Japanese high speed train concept; they were the first to introduce over 200 km/h running on a regular basis and have kept at the forefront of high speed train technology with their German and French counterparts. However, the Japanese HSTs have always been multiple units in the original sense, having many power cars distributed along the train.
The HST name was first used for diesel multiple unit passenger train developed in the UK for 125m/hr running. It is now generally accepted as the definition for any passenger train scheduled to run at over 200 km/h. For more information on the different types, see our High Speed Train Page.
This is the name given to the elapsed time between trains passing a fixed point in the same direction over the same track. It is usually expressed in minutes e.g. "trains were running at a 4-minute headway". Another way of expressing it is as trains per hour (tph).
A well run railway will conduct research to determine how many fare paying customers are likely to show up at various times of the day and will operate their trains to suit. See Train Service Planning below. In many instances the patronage numbers will show that it is possible to run trains at even intervals or at a given "headway". This may be at two hours for a long distance, main line route or two minutes for a metro.
Once established, the headway is used in calculating the number of trains required for a particular service, the train performance requirements and signalling requirements.
Terminals, Loops and Turnbacks
There are three ways of turning a train requiring to reverse its direction at the end of a trip. First a simple change of direction where a locomotive is placed at the other end of the train or, where driving cabs are available at both end of the train, can be achieved in a train in a single terminal platform with a track on either side as shown left.
Second, you can drive the train around a loop track beyond the terminal station - provided you have the space to build the loop (diagram left).
Finally, you can provide a reversing track (or turnback, as it is called in the US). The train deposits arriving passengers in one platform and goes forward to the siding where it changes direction and then proceeds into a departure platform. In the diagram below, a single reversing track is shown at the left hand end while the double set of reversing tracks are shown at the right hand end. The latter is the usual option and can be seen in such places as Paris Metro and Tokyo Underground and London.
The first option - a simple reversal procedure - is the most popular since it uses least space and is reasonably quick. For the second option, tram or light rail operators who equipped their trains with a cab at one end only favour the loop. Some metro operators also use it, notably Paris and New York.
The third option is a reversing or turnback track as shown above (left hand end) but it is often used also when turning trains at a location mid-route. The siding is provided beyond the station between the main running lines and is connected to both, as shown below.
This solution is popular for urban and suburban systems where the inner section of a route has a requirement for a higher frequency service than the outer section.
An alternative layout is where a two-track terminus has its tracks extended beyond the station (diagram left). This arrangement allows trains to be stored between the peak hours or at night. A defective train can be stored there until it can be repaired or sent back to the depot.
Train Service Planning
Here is an example of how a train service is planned for the peak hour of a short metro line. I suppose we could call it the Forest Line. The diagram below shows the elements involved in planning the train service.
First, you have to find out how many passengers will use the service. This involves assessing the numbers of people in a given area who will come to the station during each hour of the day and how they will get there. Some will walk, some will use a bus service (if there is a good connection) and some will drive, if there is cheap parking. For walkers, 500 to 800 metres is about the limit. Bus users will usually prefer to get a direct route and good integration of transport will allow bus routes to be organised to feed rail stations. Often, this process requires political commitment - essential if the resources are to be used properly.
The next stage is to determine where the people want to go and when. For planning a new railway, this will be critical in deciding the best route. For existing lines, the development of the city may already have resulted from the routing of lines as it did in New York and London.
All of this "origin and destination" patronage data is fed into a computer program and the numbers for each station, each direction and during each hour are derived. Such programs are usually owned by consulting companies who are engaged to do the work or who licence the operator to use the software. The end result is a set of numbers for each station which show:
- Passengers boarding trains in each direction
- Passengers alighting from trains in each direction
- Passengers riding on trains between stations for each direction
- Passengers transferring from line to line at interchange stations (if any)
To allow the train service to be planned, the patronage study generates "passengers per hour per direction" (pphpd) as shown at the top of the diagram above. In our case, we see the passenger numbers travelling between each station but, for simplicity, only the eastbound direction. The "curve" generated will not necessarily look like the one above on a suburban route, where there is often a build up starting at one end of the line which carries on building up until the terminus is reached and the train is full (to bursting sometimes).
Round Trip Time
Once the patronage is determined, the train service has to be planned to carry the people who turn up. During the peak hours, this can be a lot of people. The frequency and number of trains required has to be calculated to match. First the run times are worked out, again by a computer program which includes the profile of the line (curves, gradients, station locations, dwell times at stations etc.) and the performance of the trains to be used. On heavily used lines, the program may incorporate the patronage figures to estimate the number of seconds each train has to stand or "dwell" at each station while loading and unloading takes place.
The diagram of our imaginary Forest line above shows in red the computer generated arrival times, in seconds, for a train running in each direction. Added together and with allowances for terminal standing times, the program will eventually provide a "round trip time", i.e the time it takes to run from one end of the line to the other, wait at the terminus, run back to the starting place and wait for the next round trip departure time.
In our example above, the run time from Ash to Plane is 869 seconds and the time back from Plane to Ash is 871 seconds. There is a 120 second dwell at each terminus to allow the train to change direction and load/unload passengers. This is actually longer than needed but we usually leave in a bit of extra time for delays - known as "recovery time". This time is also used to give a round trip time to balance the service interval. The end result - our round trip time - is 1980 seconds or 33 minutes.
The next step is the train loading. First we determine the train capacity - in our example above, I have used a capacity of 700 passengers. This is a fairly small number for a modern metro line but it is used in London for some lines and for those places which have short trains. At the other end of the scale, in Hong Kong, the Kowloon Canton Railway uses over 4000 passengers per train as the planned capacity of its 12 car trains. On one occasion, 363 passengers were counted travelling in one 24 metre car.
The density of passengers also determines the total capacity. In Western countries, the standing capacity of a train will often be calculated at 4 or 5 passengers per sq./m. In the Asian context, this number rises to 8 per sq./m. Europeans want lots of space, Asians don't seem to mind so much. The standing area is the free floor area of the car, i.e. where there are no seats.
We also decide on a load factor. No train will fill with passengers equally from end to end and passengers will not arrive at stations in steadily flowing numbers throughout each hour. So, a load factor is applied. In our case, it is 85%, a relatively small allowance used in Hong Kong because of the density of traffic. Larger allowances may be appropriate in other countries.
Now we know the capacity of the train (700 * 85% = 595), it is a relatively simple sum to use the patronage data to determine the number of trains required each hour. You divide the numbers of passengers travelling along the busiest section of line (11,500) by the train capacity (595) to get trains per hour (19.32). We have to call it 20 trains per hour as we can't run 0.32 of a train. Twenty trains per hour is equivalent to a train every three minutes or a 3-minute headway.
Rolling Stock Calculations
We are now ready to calculate the rolling stock requirements. To find out how many trains are required to operate a regular interval passenger service, the following simple formula is applied:
Round trip time divided by the headway.
In our Forest Line example above, the round trip time is 33 minutes and the headway is 3 minutes, so we need 11 trains to operate this service during the hour when there are 11,500 passengers travelling over the busiest section of line. Some railways keep a "service spare" train on standby, in case a service train becomes defective or a disruption to the service leaves a gap in the headway which needs to be filled temporarily. In this case we might plan to have 12 trains available for service and we will have to add one or two extra to cover maintenance requirements.
After the peak hours, the numbers of passengers will drop so the train service can be reduced to match. This will often mean, for a metro line, about a 40% or even a 50% reduction in the number of trains required. The planned train loading will usually be reduced during off-peak hours to allow a greater percentage of passengers to get seats, so the number of trains operating in off-peak hours may not match the patronage exactly as it does during the peak. Thus the load factor may be 50% or less.
Rolling Stock Operation
The stock required to operate a regular passenger service will be calculated as we have seen above and then a series of "diagrams" or working paths for each train will be designed. These will take into account:
- the location of the depot
- the location of other stabling points
- the frequency of exterior washing required
- the frequency of maintenance inspections
- other routes where the trains can be used
A train will have to be given time to move from its stabling point to the first station where it is required to pick up passengers. Time will also be allowed for its return to a stabling position, its "dispersal". Trains used to cover a weekday metro or commuter service present complicated patterns of use which look like this:
All day use: AM start to night finish
Peak only: AM start to AM finish; PM start to PM finish
Peak and evening: AM start to AM finish; PM start to Night finish
Mid-day: AM Start to PM finish
Each train will be used on one of the above patterns, of which there will be several varieties.
Rolling stock must be "balanced" at the end of the traffic day and timetables must be designed to allow this. "Balanced" means that any place where trains start from (a depot or sidings) must have an equal number of trains restored to that location at the end of the day. Here is an imaginary example:
Our Forest Line (shown above) must provide 12 trains for
the morning peak service each weekday - 11 for service and 1 spare. Of these, 7 are
stabled at Ash Depot, 1 at Oak sidings and 4 at Elm sidings. One of the four at Elm
will form the spare train. Therefore, by the time the last train has stabled after
the close of traffic, 7 trains must have got back to Ash, 1 to Oak and 4 to Elm. The
timetables must be designed this way and crew duties have to be arranged so that people
are available to start these trains up each morning. If there is a train short at
any location because it was left at the depot for any reason, a trip or two will be
cancelled while the crew goes "away from home" to fetch it. This is what
it means when you hear that the service is disrupted because "trains were in the
wrong places" in the morning after a serious problem. It's the railwayman's
version of a hangover.
Another point to realise is that it will be necessary to ensure that all trains return to depot within 2 or 3 days so that they can be washed and maintained. The balancing act must therefore ensure that the trains rotate through the depot in this 2-3 day period. Performing this balancing act is made easy by use of a technique known as diagramming. Before the diagrams are worked out, a timetable has to be prepared.
To show everyone concerned - sample here - how the train service will operate and where the trains will start and finish, a timetable must be drawn up. This is not the one the passengers see, it is a detailed one for staff. It shows all details of all train movements, including empty moves and times in and out of depots. It shows each train or trip identity and intermediate times for some, if not all stations. A sample, showing the start up of the Forest Line service in the early morning, can be seen on the Working Timetable Page. This includes a train working summary and train diagrams.
This is such an old-fashioned word that many modern railway managements have forgotten its importance. In any business, the customer expects to get, at the very least, what he is told he will get. If he is told his new car will be peacock blue, he will be very upset if an Italian red car is delivered. If he is told his train will arrive at 10:05 and it arrives at 10:10, he will also get upset. Any attempt at excuses will not remove the idea that he has now formed that the railway has not delivered. He is right. Whatever other things an operator at any level does, he should have timekeeping as his number one priority.
The first premise for timekeeping is to have clocks which tell the correct time. Systems for the central control of clocks to very accurate standards are widely available and are well worth the cost of installation and maintenance and can even be used and paid for as a marketing tool. Much of the cost can often be offset by advertising around the clock displays in public places. Times should also displayed in conjunction with train descriptions and arrival/departure information. Passengers should be able to set their watches by the station clock and know that it will always be correct. There is no excuse for railway clocks which do not tell the correct time.
The definition of "on time" has been elasticised in recent years, so much so that UK main line routes have classified on-time as any train which arrives within ten minutes of its timetabled time. This cannot be held up as a good customer relations exercise, nor good railway practice. Two minutes might be considered acceptable, if penalties were to be calculated in a contractual sense.
In order to "improve" timekeeping, railways have always provided recovery time in timetables. This is extra time, above that usually required for a train to complete its trip on time, allocated in case of a small delay or temporary speed restriction. We saw this in our example above where terminal time was extended a little. Unfortunately, it has become much abused in recent years in the UK and huge levels of recovery have been built in - as much as 15% in some cases.
It does not make for good public relations when trains arrive at the outskirts of a city 10 minutes early and the passengers have to cool their heels in a stationary train knowing that they are only a few minutes travel time from their destination. Recovery time should be strictly limited and eliminated altogether when possible. It should not be used as an excuse for bad timekeeping.
Terminals are usually located in densely occupied areas and often date from an era when land was cheaper than it is now. Opportunities for expansion are limited so, for busy terminals, efficiency of operations is very important. It is essential that trains do not occupy a platform for any longer than necessary to unload the arriving train and prepare it for departure.
Trains may require cleaning and/or reprovisioning whilst in a terminal platform, since the old practice of removing a train from the arriving station at the end of every trip, cleaning and restocking it for catering requirements and returning to service for a later trip, is inefficient. Toilets may also be drained and provided with clean water in terminals, if special facilities are provided. Diesel refuelling is generally done away from the passenger areas.
Track layouts at many terminals are complex and compact, due to the shortage of space. Flexibility of operation requires careful design of the layout and short run-in and run-out times. Restrictions due to signalled protection systems for dead ends will restrict train movements at peak times. A peak hour platform occupancy of more than four trains in the hour is unlikely for long distance services. Main line terminal operators would think they were doing well if they could get a platform utilisation of three, long distance EMU trains an hour in a dead end terminus like Victoria (London).
For metro operations, terminals are usually small and can accommodate a much higher frequency of trains. No dwell time is lost at peak times because of cleaning or catering. A two-platform terminus with a scissors crossover of suitable speed (as provided for Central, Hong Kong MTR) can allow a service of 34 trains per hour to be reversed if special crewing arrangements such as "stepping back" or "double-ending" are used.
This is a crew change system used at a two-track, island platform terminal to reduce train turnround time. When the first train arrives, the driver shuts down the cab and alights. Another, waiting driver, immediately enters the cab at the other (departure) end of the train and "opens up" the cab ready for departure. The first driver, meanwhile walks to the departure end of the opposite platform. When a train arrives in that platform, he enters the rear cab, waits for the arriving driver to shut down his cab and then prepares the rear cab for departure. When this is done the train is ready for departure. It should not be confused with double-ending. It has been used at, for example, Brixton (Victoria Line, London) and Central Station (Tsuen Wan Line, Hong Kong MTR) to good effect.
This is another method of turning trains quickly at a terminus. A train (assuming there are drivers' cabs at both ends) is provided with a driver at each end to give a rapid turnround.
In the most common scenario, the train arrives at an arrival platform in a terminus with one driver in the leading cab. A second driver boards at the rear cab while the passengers are alighting from the train. The train is driven into a siding beyond the terminus by the first driver. As soon as he has stopped the train, he shuts down his cab controls and the second driver at the other end immediately opens up his cab. As soon as the route into the departure platform is cleared the second driver takes the train into the platform where passengers board and the other driver alights. This method is much favoured by the Paris Metro. Indications in cabs, such as an "Other Cab On" light, are usually provided to show when the other cab is switched out or "shut down", as they say.
Sometimes, the same procedure is used but the second driver joins the train at the station before the terminus and the change of direction is carried out in the terminal platform instead of in a siding. The disadvantage of this method is that boarding and alighting passengers are mixed on the same platform. This can defeat the object of double-ending, which is to reverse trains as quickly as possible under heavy traffic conditions.
And then there's the way it's done on the Toronto subway: each train carries two drivers at all times. The one who isn't driving operates the doors. This is normally done from a position 2 cars from the rear of the 6-car train, but it can be done from any cab. So if an quick turnaround is needed, the rear man just moves to the back of the train before the reversing station and the front driver closes the doors from what was the front cab before moving up two cars.
See also Stepping Back.
The person in front who (usually) controls the movements of the train itself. In the US known as the Engineer. Sometimes referred to as a Train Operator on metro systems or where One Person Operation is used. Also known as a "motorman" on some electric railways.
Formerly (in the UK and some other places) the Guard. Provides assistance to the passengers and driver or other trainmen. Often used for fare collection and/or ticket checking. Used is emergency to provide train protection assistance. Some railways qualify guards/conductors for limited emergency driving.
American nickname for driver.
US name for a person working in an engine shed under the operating foreman. This is in turn derived from 'Ostler' who looked after the horses for the mail coaches, so it's a survival from English practice.
Originally employed on steam locos to maintain steam pressure and assist the driver with the operation of the locomotive. Now retained on some railways as the driver's assistant, particularly on longer distance or freight operations. Called "second man" in the UK and "chauffeur" in France.
Anyone who works on the train as a normal occupation.
Crew Hours And Numbers
The basic working day for industry world-wide is 8 hours. A break in the middle of this will usually be for at least 30 minutes. On a railway operating 18 to 24 hours a day, trainmen will have more flexible working conditions which might extend the working day to 12 hours with suitable rest breaks. Certainly, shift work is involved. Many countries have laws which limit working hours and which determine minimum rest periods.
Hours can now be a lot more flexible than used to be the case, since a lot of new agreements have been worked out between staff and managers of the new breed of commercially oriented railways. However, any disruption of the service can quickly disrupt the crewing as well as the train positions and action must be taken to adjust crew working with the available staff.
It is necessary to keep some spare staff on duty at all times. Any level between a minimum of 10% and a maximum of 25% for special circumstances might be considered necessary. One can be amazed at the levels of spare crews allocated on some railways.
For an even interval service with peak and off peak frequencies, the number of crews required to be employed can be calculated by the number of trains for the peak hour times a factor of 5. This allows for training, weekend cover, occasional days off, leave, compensatory leave for working public holidays, sickness, shunting duties and spare crews. Individual totals will vary with the service provided and the conditions of employment and you might get that factor down to 4.5 or even 4 on smaller operations.