In short: A marine terminal is a queue with very few servers, so waiting time rises convexly with berth utilisation and the last few points of occupancy buy far more queue than the first ones did. Demurrage is a partial view of that cost, since it captures what is contractually payable on chartered tonnage and misses schedule disruption, tank congestion and the optionality lost while vessels sit at anchor. A berth can be unavailable while it stands empty, because tank availability, product sequencing, pilotage windows and weather all block a berth that shows as free on the plan. How much notice the terminal gets changes the outcome more than most operating levers, since a call known days ahead allows a sequencing decision that a same day arrival rules out.
A vessel arrives, waits three days at the anchorage, and the demurrage claim lands six weeks later in a different department's cost centre. The same month's terminal report shows berth utilisation at 87 percent, up two points on the year, presented as an improvement in asset use.
Both numbers are accurate and they describe the same system, where the waiting outside the port is the price of the utilisation inside it. The relationship between them is well understood, it is steeper than most operating intuition allows, and almost nobody reports the two figures on the same page.
The terminal is a queue with very few servers
A marine terminal has a small number of berths, arrivals that are irregular even when they were programmed a month ahead, and service times that vary widely. That combination has known properties, and they do not match how capacity gets discussed in a management meeting.
Service time variability at a liquid bulk terminal is unusually high. A 30,000 tonne parcel and a 130,000 tonne cargo differ by more than a factor of four in occupancy before anything goes wrong. The realised loading rate varies with which tanks are lined up, whether the product needs heating, how many grades are in the parcel, and whether the vessel's or the shore pumps are governing. Add hose connection, inspection, documentation, ballast operations and cast-off, and the coefficient of variation of berth occupancy time is frequently above one, meaning the standard deviation of service time exceeds its mean.
Arrivals are irregular too. A laycan is a window of a few days rather than an appointment, weather delays a departure upstream, a previous port runs long, and a vessel speeds up to protect a window it might otherwise miss. What reaches the terminal gate is closer to a random arrival process than to a schedule, even when every vessel on the list was agreed weeks earlier.
Why the last few points of utilisation cost so much
Waiting time in a queue of this shape is well approximated by three multiplied terms. The result traces back to Kingman's 1961 heavy traffic analysis, and the form most operating people find usable appears in Hopp and Spearman's Factory Physics (1996).
Expected waiting before service is roughly a variability term, times a utilisation term, times the mean service time. The variability term is the average of the squared coefficients of variation of the arrival intervals and of the service times. The utilisation term is the fraction of time the berth is occupied divided by one minus that fraction. The service time is average berth occupancy.
The utilisation term is the one that misbehaves. At 50 percent it equals 1. At 70 percent it is 2.3. At 80 percent it is 4. At 90 percent it is 9. At 95 percent it is 19.
Moving from 80 to 90 percent utilisation reads on a report as a ten point gain in asset use and multiplies expected waiting time by roughly two and a quarter. Moving from 90 to 95 doubles it again. No amount of operating discipline removes this, because it is a property of any system with variable arrivals and variable service. The only ways to change the answer are to change utilisation, change variability, or change mean service time.
Two consequences deserve more attention than they usually get.
Cutting variability is normally cheaper than adding a berth. Waiting scales linearly with the variability term, so a meaningful reduction in the spread of service times does the same work as a substantial reduction in utilisation, at a fraction of the capital. Standardising parcel sizes, fixing the two or three most common causes of a slow loading operation, and pre-positioning tank line-ups all act on it directly.
Pooling berths is powerful and easy to destroy. A terminal where any of four berths can take any vessel behaves far better at the same utilisation than one where each vessel is tied to a designated berth, because the queue draws on whichever server frees up first. Product segregation, hose size, draft limits and manifold configuration are what break interchangeability, and every restriction accepted converts one pooled queue into several small ones with much worse waiting at the same throughput.
Demurrage is a partial view of the cost
Demurrage is the mechanism that makes queueing visible inside a financial system, which is useful, and it shows a fraction of what the queue costs.
Laytime runs from an accepted notice of readiness, subject to whatever exceptions the parties agreed. Whether time spent waiting for a berth counts against it depends on the charter form and its clauses, which is why the same three day wait produces a claim under one contract and nothing under another. For operating purposes the more useful classification is by cause.
Within the terminal's control: congestion the terminal created by its own scheduling, tank not ready, equipment failure, loading rates below the contractual rate, documentation delays. Within the vessel's control: arrival outside the agreed window, failing inspection, cargo pump problems, slow ballast handling. Within nobody's control: weather, tide and draft windows, port authority movement restrictions, which are commonly excepted and therefore land as a cost with no owner.
Three reasons demurrage understates the queue. Excepted time generates no claim while the waiting still happened and still consumed capacity to serve other vessels. A route with known congestion gets priced into the freight rate, because an owner charges more to send a vessel somewhere it will wait, and that premium sits inside a negotiated number nobody revisits. And delayed cargo has a value beyond the vessel: a customer delivery slips, a plant runs short of feed, a sale prices into a different month.
A terminal managing against its demurrage line is optimising against the portion of the cost that happens to be claimable, which is rarely the largest portion.
The berth can be unavailable while it is empty
Berth availability is a joint state. The berth, the line, the tank and the route out of the tank all have to be right at the same moment, and the berth is often the least binding of the four.
Tank availability with the right grade. A vessel cannot load without a tank holding the product with sufficient volume, and cannot discharge without a tank holding enough space at an acceptable grade or commingle. A full tank farm makes an empty berth useless.
Line and manifold segregation. Moving product between a particular tank and a particular berth needs a clear line-up. Changing grades on a line means flushing or accepting an interface, which takes time and creates material that has to go somewhere. A berth with the wrong line-up is unavailable for that cargo while idle.
Tank turnover. A tank cannot receive until it has been evacuated, and evacuation runs through a pipeline nomination, a truck rack with fixed operating hours, a rail slot, or a downstream unit taking feed. When the evacuation route binds, tank space binds, and the berth becomes a spectator to a constraint two steps away.
Tide, draft and daylight. Deep draft vessels at some berths move only on a tide window, and some ports restrict movements to daylight hours. Those windows interact with the queue expensively, since a vessel that misses a tide waits for the next one no matter how empty the berth is.
Berth utilisation measured as time occupied is therefore a weak proxy for terminal capacity. Two terminals reporting identical utilisation can have very different usable capacity depending on how often the other three conditions bind.
How much notice the terminal actually has
The information available to a terminal improves as the decision horizon shortens, which is the wrong shape for planning.
The usual sequence runs from an acceptance programme agreed weeks ahead with volumes and approximate dates, to a nomination naming a vessel and a laycan, to ETAs updated as the vessel steams, to a notice a day or two out, to the notice of readiness itself. Every step adds information and removes options at the same time.
Three things follow for how the schedule should be run.
The plan should be re-optimised at each information arrival rather than fixed at the programme stage and defended. A monthly berth plan built at nomination and held for four weeks runs on the least information available anywhere in the sequence.
The width of the nomination window is measurable in waiting time. Take a year of actual arrivals, simulate the same stream under a tighter window, and the difference in expected waiting is what the window is worth in cash. That turns a contractual argument into a number.
Late nomination consumes terminal capacity and can be priced accordingly. A counterparty nominating inside a short window is injecting variability into the arrival process, which the arithmetic above converts into waiting for every other vessel on the programme. Terms that reward earlier and firmer nomination are considerably cheaper than a berth.
Choosing a point on the trade-off
Every terminal sits somewhere on the trade-off between berth utilisation and vessel waiting. Most of them arrived there without choosing.
The frame is a total cost curve with two arms. Berth capacity costs capital and operating expense, and that arm is roughly linear. Waiting costs demurrage, plus the freight premium a congested terminal pays without seeing it, plus whatever the delayed cargo was worth, and that arm is convex in utilisation because of the term above. The sum has a minimum, and the minimum sits at a lower utilisation than most operating managers would be comfortable defending, because the waiting arm climbs steeply at exactly the utilisations that look like good asset management.
The reason it never gets chosen explicitly is organisational. Berth capacity is a capital line owned by projects or engineering, demurrage is an operating cost sitting in chartering or commercial, and the freight premium is inside a negotiated rate that belongs to nobody. Neither owner sees both arms of the curve, and the number that reaches the board comes from the arm that looks flattering.
Before the capital option there are cheaper ones, and each attacks a different term in the same expression.
Cut service time variability. At most liquid terminals the largest single contributor is the spread of realised loading and discharge rates. Working out why the slowest quarter of operations are slow, then fixing the two most common causes, moves the variability term directly.
Restore pooling. Every restriction tying a cargo to a specific berth costs waiting time. Some are physical and permanent, and others are line-up conventions that survive because changing them was never anyone's job.
Smooth arrivals. A slot system converts an arrival process close to random into one closer to scheduled, which acts on the arrival variability term. It needs commercial agreement, because hitting a slot has to be worth something to the party being asked to hit it.
Move the waiting to sea. Virtual arrival and just-in-time arrival arrangements have the vessel slow down to reach the berth at its window rather than steam hard and wait at anchor. The bunker and emissions savings are real, and the arrangement needs an explicit laytime treatment so the owner is not simply absorbing the delay.
The limit
Terminal throughput improvements move the constraint more often than they remove it. Add a berth to a terminal whose tank farm turns over at a fixed rate and the queue reappears in front of the tanks. Vessels berth faster, tanks fill, and berths go unavailable for the reasons above rather than because they are occupied. The demurrage number may not improve at all, and the capital is spent.
So the analysis has to cover the connected system: the supply rate into the tank farm, tank capacity by grade, the berth itself, and the evacuation route downstream. Model the whole chain, relieve the berth, and watch where the queue turns up next. If it appears immediately somewhere else, the berth was only where the constraint had been showing itself.
Two cautions apply to the analysis itself.
The queueing expressions assume a stationary process and terminals are not stationary. Arrival rates move with season, refinery turnarounds remove and restore demand, and planned maintenance takes a berth out for weeks. Feeding an annual average utilisation into the formula understates the cost, because the waiting concentrates in the high utilisation months and the relationship is convex, so the average of the function exceeds the function of the average. Compute it monthly at minimum.
And the input data usually exists in a form nobody has assembled. Notice of readiness times, all-fast times, hose connect and disconnect, completion and cast-off are recorded on a statement of facts for every call, mostly on paper or in scanned documents filed by voyage. The distributions that determine every number in this piece are sitting in that pile, and extracting two years of it is the unglamorous prerequisite for the rest.
Pull twelve months of notice-of-readiness to all-fast times, plot them by month against that month's berth utilisation, and the convex curve will be visible in your own data before you model anything.